Thomas,

First off, take your time in choosing your weapon. Go to a reliable gun shop and have them show you several models and fit a gun to you. Gun fit is very important when choosing your deer rifle. If it doesn't fit you well, then you will not want to shoot it and eventually develop bad shooting habits.

After you have found the model for you, don't worry you will recognize it the second you pick it up and bring it to your should for a simulated quick shot, then see how much you need to save for this rifle. If you stick to your present budget, you won't find much out there and you will be settling on a gun. You never want to settle on a gun as you will never be satisfied with it.

Savage makes a great no frills rifle that you can pick up at Walmart or a sporting goods store. It comes with a scope on it that has been boresighted. A really good friend on mine got one of these package deals for his first rifle about 10 years ago and he still owns it and uses it to this day. He owns more expensive rifles that shoot just as good, but there is alway something special about that first rifle, and the fact that it is a tack driver.

As to calibers, you might want to consider the 25.06. It is an excellent deer and coyote caliber.

Good luck and keep us informed on your decision!
Matt

This may sound crazy but if $150 - $200 is really all you wil be able to spend dont rule out some of the surplus military rifles. For example a 6.5 x 55 Swedish Mauser. Excellent round and high quality rifle with low recoil. You can buy bullets at Bass Pro etc. You can find them at gun shows in very good condition for $150. Only problem might be they have open sights that arent so great but you say you will be shooting at mostly short range and you can buy scope mounts for them if you want to. Thats what I started with. Now I have 3 of them and I even bought a Ruger M77 in 6.5 x 55 because I like the round so much.
Think about it!