You didn't mention what "very limited budget" means to you, nor what you'll be using the gun for. A good all around choice for not a lot of money is the Nikon 3-9x50 Prostaff
. It's a solid and bright scope, and the 50mm objective lens just adds a bit of weight, but gives you a significantly larger exit pupil. The larger size is not a detriment because you have to use extra high rings anyway on your platform. Get the excellent BDC reticle and use the Nikon Spot On Technology website
to dial in your exact load for any range.