First, you will like it and be pleased you bought it. I bought a Lite stainless from a friend last year for $450, so I think you woukd be looking at somewhere around that figure for a non-stainless with a picatinny rail.

As for aftermarket stocks, there are some on this website, plus Bell and Carlson and McMillan at the higher end. I have a McMillan A3 on my T3 based semi-custom rifle, which is superb, but will cost more than the rifle.

The factory plastic stock is actually very stiff and far better than the Remington plastic stocks, so perhaps you could just try it and see how you do?

Enjoy

Hi for stocks it has to be Mountain tactical , Grs or tier one , the only people that can sort the price out is you and your mate , for me the history of the gun which you have is worth a lot and no matter what price you pay they will be another one come up for sale cheaper in the space of a month but without the history

If it's a T3 lite it's probably worth about $500 +/-.

Try the factory stock first.  I have a T3 varmint that shoots so well I can't see how an aftermarket stock would help much more.

When I first purchased my used Tikka T3 to build into my .280 Ackley Improved, it was also a blued T3 Lite in .270 Win. I payed $450 at the gun shop, and it looked as if it hadn't been shot. With the rail and cheek riser, you could throw in a bit more of course.

As for modifications, the Tikka Performance center from Mountain Tactical produces parts and pieces specifically made to fit the T3. I'd suggest a new metal bolt shroud (factory is plastic), steel recoil lug, replacement aluminum bottom metal (factory piece is plastic) and hardened action screws, and you've already got a rail. Just about all of those will be able to be transferred to a different stock later on if you so choose.

$450 for the rifle. The pic rail is worth $20.

Steel recoil lug, proper torque on the action screws, and see how it shoots before you do anything else.

pic rails can easily cost $100…what sort of cheek riser did he put on it? If the mods are first-rate quality and what you would have wanted anyway, and the gun has less than a hundred rounds through it, I'd think that 450-500 would be a pretty friendly price.
As others said, you should shoot it and see how you like it before changing the stock- the factory stock is functionally excellent, you will hear guys complain about it but that is a 100% cosmetics issue.