Obviously a lot of location factors are at play, but a crossbow is relatively inexpensive, has plenty of ability to humanely kill a deer (if that's your intended target), and the bolts and broadheads are recoverable.

Smaller game can be taken with a .22 or .25 cal air gun, which can be far more cost effective than a standard firearm, depending on if it is a spring, piston, or pre-charged pneumatic model. Side note, Lewis and Clark brought air rifles on their famous expedition.

Check your local hunting regs for legal options!