I hunted whitetail in Eastern Iowa last year with a Ruger GP100, 6 in. barrel, .357 mag. I reload, and use Hornady XTP bullets, 180 grain. This worked on a big doe last year. I'll use this gun again this year (6 days to go!). The GP100 can be bought new for well under $400, and is a shooter with just the adjustable sights.
NEXT year, I am moving up to the Ruger Super Redhawk in .44 mag with a 9" barrel. That gun is costing me $529, before I put a Holosight scope on it.
Best part of the GP100 is that practice ammo can be had for not a lot of money (I put several hundred practice rounds through mine before I hunted it), and it's cheaper if you reload.
Once you go handgunning for deer, you will not want to go back to slug gunning. The handgun is lighter, more manueverable, and usually more accurate than a slug gun. Plus, in my opinion, it damages less meat than a slug.