1. The 7mm-08 is a short action
2. There are standard shank and large shank barrels. These will fit no mater if they are short or long action as long as they can handle the length of the cartridge. Along action will handle any length cartridge. You can fit a 30-06 barrel to a short action - You just will not be able to get them into the magazine or likely cycle through the action. You could do it and single load the 30-06 and then fish out the cartridge after firing.
3. the Stevens 200 have blind magazines - you have to feed and unload through the action.
4. I know that the 223 had lots of problems with feeding - the newer style is supposed to correct that. I am not sure if the 308 family had those issues or not. I converted both of my older 223's to single shots - no problems at all.
5. When you pick up the old style stock you will notice that the mold parting lines and the areas around the false checkering is raised and rough - rough enough to cut you under high recoil. The new style stocks are much smoother, they need no smoothing down. That is the easiest way to tell the difference. There are others, but that is the easiest. Most guys smooth down the rough part then paint the stock because it really looks bad if you do not. Painting the new style is a matter of preference, not necessity.
6. The stocks are flimsy? There is generous space around the free floated barrel, if you are getting the stock twisted up to the point of touching the barrel to throw of zero - I guarantee you are having other issues too. The fore end is the part that will twist, it will not move up and down. The stock may not be "stiff" but it is stiff enough under almost any circumstance.
7. The action is pillar bedded from the factory - old or new. If you are going to bed the action just give it a skim coat and some behind the recoil lug. You might want to put a mound of it at the barrel tip, just short of the tip while you are at it. Some rifles do shoot better with up pressure and you will be able to shim the barrel from the mound you made. Just wrap the barrel with some thick (3/32" or so) no stick (or some thing you can put release on) material at the mound and let it set along with the action/lug. When you take it apart pull the thick material off and your barrel will be free floated and if you want you can shim it up for some up pressure.
8. You are correct about the tools needed. It is a little intimidating your first attempt, but it is easy and straight forward.
9. I only use a go gauge. I tighten it up against it and the back off 1/32 of a turn (about .002"). Really I just back it off very little, I feel it bottom out and then just back it off very little, trying not to let the barrel turn any while tightening it down. I check after setting the barrel again with the go gauge and with a full length sized case or a new case to make sure I backed off enough. I get very little case stretch and the cartridges go in with out resistance.
Good Luck and Good Shooting