As has already been said, the rifle doesn't make the hunter. Practice and skills do. Get the Stevens in a good all-around caliber and get good quality rings and a scope for it. The Elite 3200 you mentioned (assuming a 3-9x or so) or a Sightron SII would be a great match for the rifle. When you mount the scope, make sure that it's mounted in the right place for you. Do this by closing your eyes and them mounting your gun to shooting position. As soon as you open your eyes, you should have a full and clear view through the scope. If it's not, change it so that you do. If you're not looking through the center of the scope, change the height of the mounts until you are. If you don't have a full view through the scope (big black ring around a tiny circle of light), change how far forward or back it's mounted in the rings until you do. Never change your shooting position just to be able to see through the scope! Make it fit you, not change you to fit it. As for the trigger, just carefully follow the directions and adjust the trigger on the Stevens to suit you. Careful adjustment will get you a good (but not necessarily great) trigger pull.
Then, and
most importantly, spend a big chunk of that money you saved over buying the Tikka on ammo so that you can practice with your new gun. I don't just mean sitting at a bench at the range. I mean shooting in the positions you're likely to be using when you're out hunting. Amazingly, I never seem to have a solid bench and my benchrest equipment around when I have to take a hunting shot, so the only bench shooting my hunting guns get is sight-in and load testing.
The first month or so that you practice doesn't even have to be with live ammo. Since you are far out of practice with shooting
and you are getting a new gun, you should probably dry fire practice as often as is convenient with the new gun. One of the most important aspects will be getting used to the trigger, no matter if it's a factory trigger or a top-of-the-line match trigger. For the first week after I get a new gun or change a trigger on one, I practice dry firing with my eyes closed or in a dark room (so no temptation to concentrating on sighting) just to learn the trigger. The only thing on your mind should be feeling that trigger. I usually do three sessions a day (1st = 20 pulls, 2nd and 3rd = 10 pulls each). Once you're comfortable enough with "dark" dry fire practice, move on to sighting with dry fire practice. By this, I mean holding the gun down in front of you, looking at something specific for a target, then raising your gun into position, mounting it, holding steady sighted on the target for a few seconds until you can get a clean and smooth trigger break (no jerking!), then repeat. Once you're entirely comfortable with this (only you can decide when that is), you're ready for practicing with live ammo at targets.
As I said earlier, don't just sit at the bench and "practice" shooting. You need to practice from shooting positions. I don't know what terrain you'll be hunting, but I usually try to practice from sitting, prone (lying down head toward the target), leaning against a pole (like a tree while hunting), and totally offhand. This will also let you get accustomed to the recoil of the rifle in shooting positions, which is usually much less unpleasant in shooting positions (except for prone, maybe) than it is in benchrest position. Practicing this way also lets me know how accurate you really are, and that lets you know which shots you can realistically make from shooting positions.
In case I haven't mentioned it yet, the key here is practice. If I were taking a new hunter out hunting with me, I'd rather see him with a Stevens in his hand that he was obviously familiar with and very accustomed to shooting than a nice Tikka that had strained his budget so he couldn't afford much ammo for practicing.
Sorry for the long-winded response here, but I love to see new hunters get started the right way so that they enjoy hunting and shooting for the rest of their lives and pass on that joy to others.
