Once you stray out of the top tier brands, the similarities aren't that different. There are really only a handful of LCD manufacturing plants, and you'd be surprised to see how many TVs under different names have the same panels. Of course, the difference is in what is used to run them.
Insignia is the Best Buy house brand, which means that they've either Direct Imported it from China or go throug a third-party that does so. Westinghouse is pretty much the same, except it comes to them through a vendor.
The stats on the 32" Westinghouse look good -- for that money, it will be fine for you. It has a built-in HD tuner, which is great if you're in an area that's broadcasting HD over the air (unlike Canada, which has very little HD broadcasts -- you need to get an HD box up here). Be warned that analog channels generally look crappy on HD sets. Still, the US is going all HD over the next few years, so you're ahead of the curve.
The other thing to know is that LCD prices are dropping dramatically, and there will be incredible deals over the next few months. Black Friday will be a TV giveaway period in the US; up here in Canada, I'd suggest LCD TV buyers who can wait until Boxing Week do so -- it will be crazy.
Anyway, we're straying into my work area, and I'm likely to go on and on and on, so I'll stop now, after saying -- check out the TV in the store. If you dig it, get it. It's got a one-year warranty, so unless it is DOA when you bring it home, you should be in good hands. Hold on to the original box, just in case. If there are issues, they'll likely make you send it in original packaging to a repair facility (unless they offer in-home service, but 32" is not really big enough to justify that...). So, keep the receipt and the box for the next year, but if you're good after 30 days, you probably have nothing to worry about.
- James