Buy a nice gun and put a scope of higher value on it.
Amen, I'd rather have a 100 dollar rifle with a 300 dollar scope than 350 dollar gun with a 50 dollar scope. Which is what you will get with those package deals. Hell I don't think some of those combo scopes are worth 50 dollars.
Savage makes some accurate yet fairly inexpensive bolt action rifles. If I were on a budget thats what I would get. They may not be the prettiest girl at the dance but they have it were it counts. Good barrels and a good trigger.
Caliber? This is a matter of preference really. Are you recoil sensitive? If so a 243, 7mm-08 would be your best bet. If recoil is not a problem for you them it's hard to beat a 270 or 30-06. Ammo is cheap and available everywhere on earth with many many different types and grain weights available to choose from. I personally don't feel the big magnums are necessary for deer hunting but then thats just my opinion. I also feel that 243 is the minimum for deer.