If your kids want to play games on the PS3 then definitely get that as your Blu-ray player. The dvd upconversion, load times, and blu-ray playback are still among the top players available.
There are some advantages to a stand alone player however. They run quieter, come with a proper remote and are less clunky looking.
If you are looking at standalone, I would also second looking at players from manufacturers such as OPPO and Panasonic. I currently use the exact same model as JC, the Panasonic BD55 and have been very pleased with the entire package - how quiet it runs, load times, dvd upconversion, Blu-ray using multi-channel analog, Blu-ray video playback etc.
PS: Panasonic does not make the model 55 anymore, their new model numbers are in the 60's and 80's.