I bought a Tikka T3X Stainless Varmint (in .260 Rem) for long range plinking and short range paper punching. I have been very happy with it. I found the factory stock perfectly adequate and used it for several years, no complaints. Even though it has a relatively high stock comb, I added some stick-on velcro and a foam pad for added height for the cheek weld, which was cheap to do. I have now upgraded the stock now to an MDT XRS chassis and Arca rail system for various attachments (bipods, tripods), and to be able to use 10-round AICS mags in it for hopefully one day shooting in PRS matches. As others have mentioned the KRG Bravo chassis is also an excellent choice with many accessory mounting options.
The Tikka T3X factory stock has two M5 threaded screw holes in the forearm, (one of which has a swivel stud). I used these for mounting an Anschutz (UIT) rail, so I could use it with a Mystic Precision MPOD without an adapter. (I have a photo of this posted on a CGN thread somewhere). Also, Atlas makes the AFAR rail kit which is a Picatinny rail piece that slides into an Anschutz rail, so I could easily attach my Atlas quick release Picatinny clamp bipod to it and have some fore-aft adjustment. I could have also used those same two holes for mounting an Arca rail. In other words there is alot you can do with the original factory Tikka stock, and not blow the budget. The chassis upgrade can wait if the budget is limiting.
In what ever rifle you chose, I think choosing a heavy varmint barrel is a must. It absorbs the heat much better than a light sporter barrel. For years before I got the Tikka, I shot my Sako Finnlight (.270 Win), which is a superbly light barrel for hunting. Cold bore shot and the next few shots would consistently be very accurate. But then that thin sporter barrel would heat up very fast and the rounds would start stringing and group size would degrade rapidly. Alot of my shooting time with the sporter was spent doing nothing waiting for the barrel to cool down.
All barrels will eventually heat up mightily with high round counts on a hot day. But with a varmint barrel I find there there is more time to shoot and less time to wait for cooling, and even when hot the barrel is more forgiving and resists stringing rounds.