Most has already been said on this topic. I own a Remington 700 in .243 with a Leupold 3-9 scope and think it's a great rifle - for your whole lifetime. If I was planning on shooting it at 200# deer I'd consider a .270 also, but a .243 with 100 grain bullets will get the job done just fine too.
Buying a .22 first and shooting it is a good option. However, I believe that instead you could just get a .243 as a first rifle. The kick is not bad, most people wouldn't flinch with it. I believe that if you were to take the money you'd spend on your .22 rifle and instead just buy more .243 or .270 ammo and have 300-500 rounds down the barrel you'd be better served.
The worst thing you could do is not have practiced enough with your deer rifle.