Just Snagged a Micro Seiki DD-35 - Need Help With Affordable Cartridge Options for SM-505

Pictures worth a thousand words, here what I’m working with:

https://imgur.com/uVoifzg
https://imgur.com/IXPdhA6
https://imgur.com/tXL2pjW

Do any components look to be missing or damaged from these pics? It just seems like the cartridge should push into the housing on the tonearm another 1/2" or so. I don’t want to push too hard and do damage, but I put some pressure on it and the cartridge didn’t go in any further. Thanks again. Glad to know it’s compatible and hoping that I'm dealing with operator error here!

Push and lock, this is how it works. 
This is standard headshell and standard tonearm for this type of headshell. You can't damage it, maybe it's just too tight, but it's great for connection of the headshell pins and tonearm pins. Push and move the ring to lock it.  

Thanks guys! Good news! I took some sandpaper to the post on the cartridge and after that it slid right on! Ordered a cheap replacement stylus (don't have one currently) on ebay for $10 for testing purposes and if everything is mechanically functional, I'll order a nice setup!

Any basic maintenance I should do while I wait for my stylus?

I've got Deoxit for plastic sliders (has lubricant) and regular contact cleaner. The veneer is a bit chipped on the front corners. Not sure that can be repaired, so might just leave it looking rough... maybe some wood conditioner or polish to bring out the shine?

Well first off congratulations! That's a $300 to $500 turntable which I'm sure nobody at Goodwill knew so you must have got a helluva deal and now have a beautiful vintage table worth putting a little time and money into. Well in your case more time than money! lol!

Good. Way it should be.

Big chips can be filled with wood filler, sanded and stained. But often times less is more. Merely darkening the chips with a colored felt pen may be enough to hide them. Then wipe the whole thing down, anything from Lemon Pledge to Teak Oil will work just fine. That wood is probably thirsty so don't be afraid to slop it on and keep slopping it on as long as it keeps soaking in. 

Pull the platter. Clean the platter top and bottom. Clean everything. Disassemble, clean and lube as much as you can- especially the bearing, footers, arm, and whatever suspension you're able to find. I don't know that model but just based on vintage there's probably springs and/or rubber parts. Be careful. Some plastic/rubber parts may be brittle or cracking. In those cases may be better to carefully preserve than try and take apart and risk damage. 

Carefully inspect and check as much as you can of the wiring, every bit of it from the cartridge clips to the head shell/arm pins to the RCA connectors. Clean all contacts to shiny metal.

The bearing should be your biggest concern. Try if at all possible to disassemble the bearing, clean and lube. Failing that soak it as best you can. I have a similarly old DD table and it still works great except you can hear the bearing rumble. Well in my system you can! Maybe not with your associated components but still you will want that bearing clean and lubed it is after all nearing half a century!

These vintage tables have a pretty good following, you'll probably be able to find tips on all this if you search around enough.

Awesome! I should have a stylus by early next week and will open it up for a cleaning if it plays nicely. Very excited. I sample vinyl for music production. Currently using a Sony PS-LX520. I love the automation, but MS looks way cooler. Wonder how they'll compare...