In my opinion it really doesn't make much difference when it comes to brand, other than having the right features you are looking for. It's not like the analog days where you had to pay more money for a multi-head VCR with hi-fi sound and S-video output and get really good connectors, or what have you. The digital signal of a Blu-ray should theoretically be the same whether it is Sony or LG. I think the upscalers might be a bit different across brands but I've never heard of a DVD looking worse on a BD player than a DVD player so worst case it looks the same.

I've had experience with Sony, Toshiba and LG players. As far as I can tell they all work the same, but Sony is the most expensive, Toshiba is in the middle, and LG is the cheapest, simply because of brand name value. I'm sure if you got an LG player you would have no complaints. Check the reviews before you buy to make sure it is reliable though, some cheap models tend to skip or have long load times but LG is a pretty decent brand, especially for the price you pay.