While I do Agree with every one's suggestions that they have made here, my personal preference for deer hunting is a customized AR platform. The reason for this is
A). There is no bolt, so you don't have to take your eyes off of the target
B). While rather expensive when compared to the other rifles suggested here, the AR platform can be easily converted into a Home Defense weapon that every one in the family can use, from you with your, I assume, man hands, to your wife.
C). The AR is easily disassembled, has only 3 main parts: bolt, cocking handle, and bolt spring located in butt stock. As a sub-side of this, you can switch out the barrels for .308 and .223 for different types of game.
D). The AR is the most popular platform in the U.S, which means there is really no limit to spare parts should your rifle break down.
E). The AR can mount various accessories for hunting such as night vision optics ( I use these for hunting wild boar), scopes, bi-pods, butt stocks with raised cheek rests and so forth.
D). I have seen versions where there are AR-15's with 7 inch barrels, which I know, isn't much use in hunting due to decreased accuracy, but you see what I'm getting at.
*Update
Didn't notice the $400 budget there. While I do know this rifle is nowhere near that price range, I'm just throwing it out there that it is worth taking a look at...