As always you are going to want to stick with name brands you are familiar with, unless you do your research and check the reviews on other brands.
Secondly, when choosing a blu-ray player you want to make sure it can up-convert normal DVDs to 1080p, that way older movies look almost as great as blu-ray discs on your HDTV.
Thirdly, it is a good idea to purchase a blu-ray player that can connect to the internet, that way it stays up to date and can fix any problems or add new features as time goes by. Also if it is capable of having applications or other internet features that is a plus as well.
The blu-ray player does not have to play 3d blu-ray discs, unless you have a 3d HDTV. But if the blu-ray player you are looking at has that capability, it is a great feature to have just in case you decide on getting a 3d HDTV in the future.
If your looking to get the best picture out of a blu-ray disc, make sure the player you decide on can output picture in 1080p/24p.
Click here to learn about how to get the best picture and audio from your HDTV and Blu-Ray player using the right cables.
...or looking to get a new blu-ray player and HDTV at the same time Click here to learn what to look for when deciding on a new HDTV.