Best Tonearm and Cartridge for 4K or under for restored Garrard 301

I have gone down this route. I have a restored Thorens TD124 and Garrard 301 rimless grease bearing. First, I echo Millercarbon and Chakster, though I lack the experience Chakster has with a wide range of arms. I have two Reed 3P's. There is nothing more important than an arm that is easy to set up. Reed supplies levers for each and every adjustment. Loosen a knob, adjust a lever, and bang, you're done. Reed has a unique design on the bearing assembly which is not quite a bearing assembly. 
News flash-despite the success, the Fremer Video-which I own-is so basic that it is practically useless. Properly setting up a table is not like watching a Youtube video to learn how to replace a cartridge valve in a faucet. Getting azimuth, VTA and SRA optimized takes a ton of hands on experience and special tools. My advice is to hire a pro. That is what I do-Brian Walsh. If you buy a Rega or VPI Scout or similar, sure, that basics will do because you have a basic table. But if you are going to the lengths that you are going, don't waste that great deck and arm with a mediocre to bad set-up. 
I have used Jim Campbell. He worked on my TD124 before many years later deciding to have it worked on again, this time by Greg Metz. He is a great guy. His forte', in my humble op, is building plinths. Do you want your Garrard cleaned up the proper way? I mean really cleaned up and restored? There is Ray Clark of Classic Turntable Co. in Wakefield, Jolly UK (I bought a bunch of aftermarket parts including his power supply and have talked to him) and there is Greg Metz of STS just outside Nashville. These two will strip your Garrard 301 down to the parts, if necessary sandblast your chassis and repaint it. These two know every trick there is to restore a Garrard to like-new condition and which after-market mods are worth the money and effort. Greg is an absolute technician and stickler for precision when it comes to working with turntable mechanisms and parts. 
I don't want to take any business away from Jim Campbell, but most Garrard 301 experts will tell you that slate is not the best choice. Sure it sounds like a great idea, but that doesn't mean it is optimum. Steve Dobbins out of Boise Idaho is a noted Garrard 301 expert. He supplies a plinth known as the Dobbins Plinth. I used Russ Collinson, again in Jolly Old England, (Layers of Beauty) to build a huge custom Shindo-like plinth with Cocobolo veneer. If you go to Russ' website, you can find a video of him applying the veneer to MY plinth. Everyone who has seen it, including Brian Walsh, say they have never seen a nicer one. My point being that imho layers of proper wood are better for Garrard 301's than slate. The Garrard 301 needs to be tuned with complimentary sounding components, not deadened. 

Kanchi;
First, to respond to your response to Chakster, I have a 12" Cocobolo Reed 3P on my Thorens TD124. It is not a high mass arm. Reed markets the different woods as having different masses and there is both an element of truth and an element of misleading marketing there. All of the Reed 3P's regardless of choice of wood are medium mass afaik. Every cartridge I have mounted on my 12" Cocobolo has absolutely sang-including my two Benz Glider LO's which frankly never sounded good on three different VPI arms I used to own. I am currently using an Ortofon Cadenza Bronze on that arm and it sounds great. 
Now as to plinths. Of course Oswald Mills is going to tell you that there granite plinth is best. I believe they will also sell you a cast iron plinth that got press in S'Phile not long ago-though that may only be for the SP10. You read that constrained layer damping is not a good idea for Garrard? Well, how do I respond to that? No offense but you can read all kinds of things on any subject-but they are often not true. Plus, there is no right or wrong. It is a matter of taste. Do you want your Garrard 301 to sound fast, clean, and sterile (admittedly this is somewhat of an exaggeration but I need to express characteristics associated with such high mass inert plinth materials mated to the 301) or do you want it to do the best possible job conveying tone and texture? 
I will give you an analogy; take a look at Jason Victor Serinus's system and his reviews in Stereophile and compare it to Art Dudley's. Or go listen to a system with Magico's powered by CH Precision electronics and compare it to an all-Audio Note UK system. There is no "perfect", there is no "correct" and there is no "does everything the best". You have to choose what you want and what you are willing to give up. Just as with loudspeakers to use yet another analogy. You can't have it all. 

Just curious Kanchi-did you look at my system on my profile page and particularly my Garrard 301? If you prefer noromance’s, my feelings will not be hurt but....
The idler wheel is rubber on steel. http://www.audiosilente.com/garrard-401-idler-wheel-garrard-401.html
"They are a bit expensive and shipping"? Perhaps you mean with shipping. This is no time to be looking to save on things. If you want it done right, you have to pay for shipping. I bought a lot of things from the UK, Ray Clark’s PSU for the Garrard, my plinth from Russ, shipping is not that terribly expensive.
Hell, I got in the car twice and drove six hours each way to pick up my decks from Greg in Nashville. Worth every minute of my time.

I bought my Garrard 301 from Greg. Greg says he found it at an estate sale in essentially NOS condition-as if it had barely been used if ever. He cleaned it up and installed an AudioSilente idler and an SMD Acoustics main brass bearing from Peak Hi-Fi at my request. https://www.peakhifi.co.uk/cgi-bin/ecom.cgi?Command=ShowProduct&db_pid=718
Greg does not build plinths and does not particularly enjoy even dealing with plinths. He did recommend the Ray Walker PSU and so I bought one, had it shipped to Greg, and Greg assembled the wiring to make it easy to integrate  https://www.classichifi-shop.co.uk/product/classic-301-401-power-supply-unit-psu/
I kept the old grease bearing since it has virtues of it's own that I may wish to take advantage of someday. 
I then ordered the plinth from Russ Collinson and installed the Garrard chassis into the Russ Collinson plinth and then gilded the lily by adding this beauty  https://www.peakhifi.co.uk/cgi-bin/ecom.cgi?Command=ShowProduct&db_pid=1258

Now on my Thorens TD124, it was entirely different. It had been in my family for 60 years since my dad bought it brand new in 1959. It needed a lot of TLC. Greg stripped it down to the chassis and parts, had the chassis sandblasted and repainted to original cream color and at the time, Greg was able to supply a massive machined aluminum platter and custom bearing of his own design. He supplied the plinth and took all the steps necessary to implement the 12" Reed 3P including having a custom pillar pod machined to raise the arm the necessary height for the thick platter (something rather unique to TD124's where the chassis is elevated over the OEM platter more than usual). It too got a bunch of after-market parts including the AudioSilente idler. Greg's real passion and expertise is with Thorens and the 124. He studied repair of the 124 in Switzerland under one of the former Thorens technicians for several weeks many years ago. 

You are best off shipping your project to Greg and then only going to see  him when the project is done and ready for pick-up. He lives out in the boonies and prefers to meet at neutral locations. I never asked but assume he prefers his privacy and that his house and workshop are exceedingly difficult to find if you are not a local. 

And last, I live in suburb of Columbus OH. If you are ever nearby and want to see/listen, just PM me. 

Please tell Greg Mitch from Ohio referred you. 

@pindac;
A very heavy platter, like my solid brass platter from SMD will eliminate virtually all of the bass emphasis but sacrifice a good bit of the propulsive quality that many of us love about our idlers. With my current cartridge, a VdH Colibri Crimson, I like the trade-off but I am sure as hell not getting rid of my OEM platter. My current 301 set-up renders tons of detail and clarity at the expense of tone and midrange warmth. As I said above, no one turntable-despite what one noted analog expert would have us believe-provides everything. The same holds true for every individual component known to mankind, every phone cartridge, every system, and every room. 

I'm also sorry, but your argument about the effect of a high mass counterweight is specific to FR and Ikeda, and I am talking in general about the calculation of tonearm effective mass. A heavy CW, which because of its weight can be placed close to the pivot, can have the effect of reducing effective mass, because the factor of distance between the center of mass and the pivot is squared, whereas CW mass is to the first power. Those are facts. Ikeda didn't abrogate physical laws. If you want to minimize effective mass, you are best off with a heavy CW that can be placed as close as possible to the pivot vs a lighter CW that has to be further from the pivot to achieve balance or the desired VTF. That's all I was saying.

I believe the point you are making is analogous to the point Mike Fremer and others make about the inherent superiority of 9" arms over longer arms to minimize latent reaction to groove modulation and warps in the vertical plane. That on paper may well be true, but in actual practice there are advantages to 10.5 and 12" arms and as has been a common theme in my posts on this thread, you have to pick your priorities. Are Koetsu cartridges with heavy stone cartridge bodies inherently inferior to lighter cartridge bodies since they require larger CW's to balance out? Common sense tells us the answer is no. 

fsonicsmith

... the inherent superiority of 9" arms over longer arms to minimize latent reaction to groove modulation...

Will you please explain what "latent reaction to groove modulation" is?

I can’t tell if that is snark or not. The concept is that due to higher mass, a 12" arm can not react as quickly to changes in the vertical plane. Those that believe it is a real issue claim that the compliance of the cantilever is insufficient to eliminate the effect. There is no doubt, as a matter of physics, that the advantage of a 9" arm in this regard is real. The question is whether in reality, a mere 15 to 30% of additional arm length makes an audible difference and one that outweighs the advantages of lower tracking error.