CTR (Compact Tactical Rifle) is a flavor of T3X.
Budget?
For an accurate, easy-to-find, out-of-the-box, go-shoot-it chassis rifle, it's hard to go wrong with a TAC A1. I had one as my first "serious" centerfire rifle and sold it (in one day) only because I had an opportunity to pick up a fully-built custom at a great price. I still have a T3X Varmint (.223) in an MDT LSS-XL chassis. Suitably accurate (pretty much any decent bullet shoots into 0.5" or better at 100 yards; handloads hold 1/2 MOA or better out to 300 yards easily - past 500 on calm days when I'm living right.
Many people advocate buying a CTR and putting it into a chassis of choice. If you want to stay with Tikka forever - and some do - it's not a bad plan. But Tikka chassis fit Tikka actions and nothing else. For down-the-road versatility, R700-footprint actions are my personal recommendation. Emphasis on my recommendation - and it's based on my personal preferences. Other preferences/recommendations are just as valid.
Action is the same across T3X rifles but barrels vary in length. I don't know about contour. For me personally, I see no sense in putting a short barrel ( under 24") on a 6.5CM - too much velocity loss. Again, my $0.02 and other opinions are different.