First of all, let's repeat the general optics rule: "With optics, you get what you pay for." Yes, this is a general statement and there are exceptions. For example, you can get a Bushnell Elite 4200 for, say, $350, or a Swarovski or Zeiss for $1,350. The Swarovski is a "bit" better in terms of optics and structural integrity, but not an extra $1,000 worth.
There is no hard and fast rule, but rifle scopes under $200 fall in the "be careful what you are buying" and "try to spend a little bit more if you can" categories. To buy a good (new) scope for $100 is going to be very, very difficult.
Forget about the BSA. A retailer has told me that his customer return rate on BSA scopes for defects exceeded 50%.
Simmons? My personal opinion of them is very close to the BSAs. I trust that there are people out there that will state (and accurately so) that they like their Simmons that they have had no problems with them. On the other hand, I know of several people who have told me that they are not good scopes. Like I said, my personal opinon is do not buy the Simmons.
Bushnell? It depends. I personally would not go below Bushnell's Trophy line. The Elite 3200 would be much better, but then again you would be spending more money.
My advice is look into the Bushnell Elite 3200. If that is too much, then look into the Nikon Buckmaster. If that is too much, then look into the Bushnell Trophy line. If that is too much, then don't buy a scope right now. Save some more money and get one of the above so that you will be happy in the long run. I'm not telling you to get a leupold Vari-X III, Nightforce NXS, Bushnell ELite 4200, Swarovski, Zeiss, etc. (although it never hurts to get top notch optics). All I am saying, per your request to speak up now, is look into those three that I mentioned. Trust me, you would be much happier in the long run. :-)
Zachary