My son has a 2 1/2x fixed on his 20 ga. tracker II[bushnell]. Been on it 11 yrs., and we have only had to re adjust sites a couple of times. I have a simmons 1.5-5x pro diamond on my 870, and it has been great, with only a couple of adjustments in the last 7-8 yrs. I also have a 2 1/2x fixed cabela's pine ridge, on my huntsman ML that has been a sweetie, too. I guess what I am saying is, yeah you can go cheap[ the above scopes were all in the $65-80 range], just don't go TOO cheap. Most likely you will get along fine.
Mad Dog