If you want to see 1920x1080 you have to have a monitor that's 24" or more, or you will have to see everything in 1280x720, these are HD formats for blue-ray play back..
Not true. If you playback a blu ray on a 1680x1050, it can take 1080p and downscale it - there aren't just discrete resolution steps that are allowed.
As for the software, I use Cyberlink PowerDVD Ultra - it came with my bluray drive, and works quite well. I have tested it on my 22", and it is definitely sharper than 720p.