If you don't plan on burning many discs, then most of the USB 3 slim drives will do ok. As a general rule, we've found the slim drives to be less reliable long term, so that might be a consideration.
I'd get a full sized LG BE14NU40 if you plan on burning lots of Blu-ray, or get a Pioneer 209DBK and put it into a Vantec USB 3 external enclosure.
Many drives come with a crippled version of Cyberlink PowerDVD which will be able to play your Blu-ray movies as long as the software is updated. Cyberlink has, in the past, been very bad about keeping the crippled versions up to date, but have changed their behavior slightly as complaints poured in on them. Even with the full versions, Cyberlink has a tendency to change the number on the software so they don't have to keep updating older software for free. But right now PowerDVD is the best option for playing Blu-ray with full menu support. The very best Blu-ray playback software has been discontinued...it was Arcsoft TotalMedia Theater. But is is no longer for sale, and no longer supported.
Most of us have shifted to using decrypters (like AnyDVD HD)in the background and playing with free software, or we rip the Blu-ray discs to the hard drive and play from there. Once free of encryption, there are many free choices for playing the movies. I prefer Media Player Classic Home Cinema, or PotPlayer, but others you might look at include the VSO Media Player, the Leawo Media Player and VLC. None of the free players are particularly good at playing menus, even if they say they can.