I hope you’re not disappointed in that 303 British. It might not be the fastest and the most powerful cartridge but it will do the job.

If you could get a little more cash, take a look at the Bushnell Trophy 3-9x40mm. The optics are excellent for that price range. The Bushnell Dusk to Dawn 1.5-4.5 x 32 mm would also be a good choice for the price range although I have never looked thru them. You might also look at getting a fixed 4x scope. Good luck in your purchase.