"...everything you wanted to do..." A great deal depends on what that is.
"...the ammo is a lot less than shotgun shells..." Nope. Roughly $30 per 20 for .308 hunting ammo, of any brand or bullet weight and you need to try a a box of as many brands as you can to find the ammo a rifle shoots best. Roughly $7 to $8 per 25 for bird shot. Slugs are more expensive, but you don't need 'em for HD. They're not great for HD anyway.
"...lack the ability to reach out..." Isn't an issue for HD. HD isn't about long range. Knowing exactly where any shot you fire ends up is far more important. You are responsible for it.
A used, rifled sighted, smooth bore, pump 12 guage, shotgun. Won't cost you a ton of money and will give you a deer gun. Typical accuracy is about 2 or 3 inches at 100 yards out of any 12 guage shotgun. Plenty accurate for deer sized game.
A new Mossberg 3 in 1 combo may be worth looking into. Gives you 3 barrels with multiple chokes for not a big pile of money. Runs about $500Cdn, up here. Less Stateside. Might as well be a grand if you don't have it.
Don't worry about buying used either. It takes a great deal of abuse to damage a modern firearm of any type.
"...an M1A..." Not on a small budget.