Hi Bryce, it helps if you give an actual number for your budget.
There are some scopes that should be totally avoided and some that are ok/useable and they start at around $100.
However, the bottom end leupolds start at around $300.
More important in a hunting scope than zoom range is clarity. For example, for a 300 yard shot, I'd far rather use a cheap 4x that's reliable and clear than a cheap 3-9 that's neither. But I can get the 4x for about 1/2 the cost of the 3-9. Fixed scopes have less to go wrong with them, and are far clearer than zooms, and all that matters alot when you have a budget scope.
Btw, the first and worst scope failure I ever had was opening day on a deer hunt with a leupold vari-x 2 c (compact) 2x-7 scope that went milky (with a rattle) at that moment when I surprised a deer at 20 yards. It was a crappy scope from day one (dim image, poor adjustments), but I bought into the leupold is the best scope marketing and was sadly disappointed as that was my only chance that season. It was a $250 scope (my most expensive at the time), and any one of my other Bushnells, etc were better scopes. I had it repaired and sold it ASAP on ebay after that.