Not saying that the quality of these scopes will be up to your liking...but they would fall into the price range and utility that you are seeking

Simmons (if you can find one) Whitetail Expedition 1.5-6 X 32 should be under $100 new with rings and mounts

Nikon fixed 4X Pro staff $ same as above

Bushnell Banners and Trophy lines have a bunch of scopes in fixed and variable that will come in under $100

I don't think you will need more than 6X but if you could find a 3 x 9 that was somewhat compact that might work for you

Personally....I'd go for a little more quality in a used scope....it'll probably last as long os the rifle. Leupold...Nikon... older Redfields...Weavers