Tube recommendations

I  am a tube roller myself .  I just got an old Antique Sound Labs 845 SET integrated with multiple 6SN7s and a 6L6GC or KT-66.  I rolled all of the except the power tubes (845s) but I am seriously looking at replacing them.  I know my tubes pretty well and figured out which combination of 6SN7s would yield the sound I wanted. 
I agree that you should listen to your phono stage to learn what your baseline is.  You never know you might be happy the way it is.  You should really know what sound you are seeking as well/  Unfortunately in your situation you need to find tubes that are dead silent. Truly silent tubes that are fairly old are not that easy to find. Phono stages pick up and magnify the smallest of signals and do the same with any noise that is present.
The other matter is knowing where you can stretch things .  For instance my favorite 12AX7 or ECC83 is neither.  It's a 5751, however 5751s have lower gain than a ECC83.  If you are only using MM cartridges you might get away with that roll.  If you need all the gain you can get then you can't. If you want to keep the sound sound clean and clear then Telefunken is a good choice, some would advocate for current production.  If you want to warm up the sound then try to find a Blackburn Mullard from as early a period you can find. There are several other levels in between.
  One of the best 12AT7 or ECC81 was  made by Brimar it's a short lived sub brand, premium tube, they  called Trustee Brand and the ECC81 tube was numbered 6060, they are still available in the second hand market.  Andy doesn't like Brimar so don't tell him I told you that.  They are excellent tubes in MHO. 
The most difficult and expensive tube you will be chasing is the excellent E88CC or 6922.  They are expensive , if you like a clean crisp sound try to get a Siemans or Tlefunken.If you choose to go with a pro like Andy at vintage tube services be prepared to spend some money.  Another excellent tube pro is Brent Jesse at Audio tubes .com (he is on vacation) There is another great pro tube seller who will generally be less expensive - Jim McShane find him on audio asylum at McShane Design.  I am not affiliated with anyone yada yada yada,

Thank you for the kind words.  The price of Brimar tubes has generally been lower than the Mullard equivalent. To be perfectly honest I haven't bought a  Brimar Trustee  6060 in many years.  I would guess that because of their scarcity that  it will boil down to you and the seller agreeing to a price usually on Ebay.  I think that $100-$150 range people have mentioned seems appropriate.  I still have 2 or 3 of them.  Which brings me to the other point people have been alluding to.  Tube rolling is indeed a slippery slope.  I too couldn't get over the fact that with most tube rolls I heard a different sound.  I liked it so much that I have a stupid number of tubes.  I suppose I should sell but then I would want to buy them back again. 
Not only did I like rolling the various tubes I was using, I then just collected them for any of a number of reasons.  I also thought I should get back ups for them.  You see how it goes-
So you can stop now or forever hold your piece.  Quite honestly I enjoy my tube collection. However,  I am still wondering why I bought so many short bottle 6SN7Ws. I have about 16 of them.
I hate selling, many of these tubes are 70+ years old and might not sound great or even good in the buyers gear.  I don't want to deal with complaints and returns, I am not a department store.  At the same time I don't like it when the seller says no returns whatsoever, or as is. as found.  I  have been burned many times by unscrupulous sellers and have bought some real loser tubes .  One prominent example is my experience buying Western Electric 421As. I was buying them for a headphone amp I bought that uses 6AS7Gs and 6080 power tubes.  So many were feeble shadows of themselves, and I got the sense that the guy was selling it was simply trying to get his money back from the last guy.  I swallowed a few and decided to look for other brands of the same construction, e.g. domino plates. I refused to do the same passing on a weak tube.  That's what honesty buys you.

You're welcome. Are you certain I can't introduce you to some o return used up crap from the last Shmegeggy, I bought them from.
Seriously, I have a major surgery coming up but in 10.5 weeks I'll be back, and for the first time seriously consider selling some of my tubes, only I will be honest about it..  I will do it through normal channels and I may indeed have an extra Trustee 6060 pair. I'll be sure to advertise them at that time.As long as I am writing in a dead thread, I will say that some microphonia in 70 Year Old 6SN7GTs isn't always a bad thing. I'll start a thread on that one, because I genuinely think and believe it helps with stage width depth and other  imagery, honestly.