I have a BSA Deerhunter 1.5 x 4.5 on my slug gun and it has served me very well for over 10 years now. Nice and clear and has always held zero with 3" mag slugs.
I haven't used that particular scope but have had a few BSAs. It's a low end scope, not to say it's bad for the money and in your situation it will probably work out fine. In my experience once you get past a 100-150yds the optical quality gets kinda crappy.
I put a Bushnell .22 Rimfire 4x32 on my sons Winchester 190. Great scope for plinking. I put a BSA .22 Special 3-9x32mm on a Marlin 60 about 10 years ago. Real good scope for a .22. I have an old contender 6-24x40mm AO on a Marlin 917V .17HMR. Great for shooting small stuff out as far as the gun will shoot.