Good deer hunting ammo that's relatively inexpensive and easy to get? I like 6.5x55, commonly called 'Swedish Mauser' ammo. Flat shooting, I have no trouble finding ammo (tho' I tend to stock up when I find a decent price $18-22ish). It's an old WWI era round, interesting because the 'lead' is very long, and has 'sectional density' out the wazoo. End result, easy to shoot round that hits like a hammer. The swedes use it to hunt 'elk' (what we call moose over here). Flat shooting, easy on the shoulder, lots of boom downrange. I've got a couple of the old Swedish surplus mausers, they're in excellent shape - and the metalcraft on these old guns would cost thousands to build today. The Swedes marched around a lot with their rifles but haven't fought anyone for a while (Gustavus Adolphus/30 year war?) tho' there were a lot of 'volunteers' who went and helped the Finns against the Rooshians. Anyway...you can find nice 1896-1937ish surplus stuff for $300 or so, but expect people to ask a lot more at first.
If you want to spend more, I'd look at a CZ in 6.5x55 instead. I have a 'full stock' CZ 550 and really love it - probably my favorite rifle. That'll run $500 or $600 new...and I never see 'em for sale used. They're sweet shooters, w/'set' triggers. Be aware - finding rings for a scope for these is...interesting. If anyone gets one of these and wants to know more about rings, holla. I like the open sights, but as my eyes change I'll probably put a scope on one of these days. She's just SO pretty as is, I hate to mess her up.