What basic bolt action rifles provide good platforms for upgrades into a very precise rifle?  I know Rem 700's form the foundation for many excellent rifles and have many aftermarket options.  What are the other options out there to start with?

Mine was a m77

Steer clear of ruger m77's. They don't make a very good donor action, not because of quality but because of shitty aftermarket support and low adoption for PR uses. A good Ruger option is the RPR. RPR fits all your desires pretty well though out of the box accuracy hasn't lived up to what I'd expected out of them.
Savage has huuuge aftermarket, lots of upgrade bits you can do, everything can be done DIY, very accurate out of the box. Some models have shitty flimsy tupperware stocks. Find one with the accustock or a Stealth with the LSS chassis.
Remington has a huuuuuuuge aftermarket, lots of upgrade bits you can do, big stuff requires gunsmith or machinist skills, usually accurate out of the box. Better trigger than Savage IMHO.
Mauser 98 foundation for many an incredible rifle. So-So aftermarket for some things & much will require a gunsmith. Donor actions can be had very cheaply.
Tikka, not so much aftermarket, just a little. Pretty kickass out of the box. Accurate out of the box. Expensive.
CZ, not much aftermarket. Pretty kickass out of the box. Accurate out of the box. Single Set Triggers, better for the hunter than the target banger IMHO.
FN, sick expensive, moderate aftermarket, accurate out of the box. I love their actions. Others may not. I'd pass for the beginner. Sink the extra money into your optic.
For the beginner a Remington or a Savage, from the factory with heavy barrel, I'd normally say grab a .223 so you can learn to shoot long range and read wind for cheaper than bigger cases allow.





If you want to actually build an ultra precise rifle then grab Defiance Deviant action, a Broughton or Hart or Lilja or Kreiger barrel, a jewel trigger, a manners (or whatever you like) stock, have Steve White of White's Gun Works in California assemble it for you. You're looking at $3000-$4000 all in but boy I mean that gun will shoot like a house on fire.
 

Excellent Info.  Thanks very much!