Main thing is to stay away from any petroleum products. They will dry up, attract dust and the oil will turn gummy. The best type of grease and oil to use is anything synthetic. I use synthetic clock oil (which is essentially the same as Ghettoboom767's sewing machine oil) on flywheel and motor bearings. The machine oil works great because it's a catalyst and really gets into bearings to protect them and will never dry up. Then Super Lube grease (as others have mentioned) where needed on gears and metal parts that slide in a channel, etc..
For the pinch roller I use Tascam rubber cleaner (available online) then follow everything else up with 91% Isopropyl. I use Deoxit for any crusty controls. You get all of this in your bag of goodies and you are all set for life
All of this will maintain and keep your radio happy for many years..mechanically that is.
I have 30 year old decks with all original parts (except belts) that still play like new thanks to using these maintenance items. I clean my pinch roller every 6 hours or so of playback time along with the heads. That's just me though. Can't stand the thought of iron oxide on my heads and a tape path on the rollers Wow and flutter will never be an issue keeping up with this routine.
One other thing. You may find yourself needing to adjust motor speed after all of this. When you are all done if it sounds good to you then I wouldn't worry about it however, if it plays slow or too fast most all motors have a tiny speed adjustment hole on the rear of the drive motor that will adjust the speed. You may already be aware of this.