.223 at 200 yards?
I don't know how great an idea it is to try and shoot deer at 200 yards with a .223. I would think that an accurate shot would be as crucial as it gets. With that being said, trying to shoot a .223 at 200 yards at a deer would be pushing the extreme edge of potential accuracy.
I use my Rem 700 VS in .308 for everything. Shooting 1000 yard matches, shooting deer, shooting pigs, shooting, coyotes, and shooting ground squirrels. I made a 325 yard shot on a squirrel this weekend that I was mighty pleased with. No cheap ammo goes into that gun anymore though. You don't shoot precision rifles to waste ammo or to plink. You shoot precision rifles to hit what you are shooting at everytime or as near as possible. Getting that out of a cheap semi-auto is not really possible.
I also took my Ruger 10/22 with me this weekend too. Out of the dozens of squirrels I shot, I shot them at 100 yards or less with the .22. Only about 4 were taken with the .308. I did the heavy plinking with my new 10/22 package I just spend way too much money on (but does it ever shoot good!), and I did the long range work with the 700. So BJ, I think you said it best when you save your money up for the .243 and its ammo and you rely on the wasting of ammo for the .22. Plus, with a bolt gun, your mission is not to hear it go bang, bang, bang. Suddenly you shoot a whole lot less and concentrate on one shot hits a whole lot more. You don't "waste" as much ammo.
The biggest factor in my choosing .308 was that I had a reloading machine and an M1A in .308 already. I make my own custom rounds for a signifigant reduction in price. Therefore it is not a problem for me to reload Hornady 110gr V-max or Speer 125gr TNT Hp for shooting varmints, Sierra 165gr Spitzer boattails for deer or pigs, and Sierra 168gr and 175 gr HPBT Match or Hornady 178 gr A-max for shooting long range. I taylor the loads to how I want them. Another extremely valuable and enjoyable part of the shooting process. Is the .308 a little expensive for shooting squirrels? Yes! That is why I don't use the .308 for "plinking". I use the .22 for plinking. I use the .308 when I want to make my shots count and want to practice accurate, precise shooting.
I think the .243 would be a great idea for you despite my personal preference for the .308 because of its versatility for just about everything. What I would suggest to you is to start thinking about investing in your future. Look into reloading. I once thought I didn't have the time or the start up capital for such a venture (and I thought I was too young). A year and a half later I do not and will never regret my decision to invest into reloading. If you want to shoot a lot of centerfire ammo, the sooner you invest in a reloading outfit, the sooner you will start saving money. Reloading is a lifetime investment and it pays off!
Go with the .243 and save the heavy plinking for the .22. And start thinking about how much shooting you want to do and how much money you want to save. Reloading your own .243 rounds to fit deer hunting or varmint hunting will save you money and give you the versatility that you are not going to find with expensive commercial ammo. The sooner you start, the more money you save.
Sorry this is so long, you know how us gun nuts get when we are talking about our hobby.