In short, 25GB blu-ray discs are single layer and 50GB blu-ray discs are dual layer. The difference in the size will be due to several factors: bit rate, length of film, extras included, alternate audio, alternate scenes, 3D, etc.
That being said, there will not be a difference in the quality of a film if you can find it on both single and dual layer blu-ray. For example, a standard edition film may fit on a single layer blu-ray but a special edition with extra features or 3D may require a larger capacity dual layer disc. The film will be the same.
For the PC vs. stand alone blu-ray players you will find very different opinions. A standalone blu-ray player usually has decent picture quality out of the box. A PC blu-ray player may be just as good upon initial setup as a standalone, or may require some tweaking to get a good picture. For example, you may need to play with the output video levels on a PC because there may be a quality difference between 0-255 levels (PC range) and 16-255 levels (TV range). It will depend on the capabilities of your TV how these are handled. Also, it's much easier to get 24p playback on a standalone player, while it can be tricky on a PC.