What considerations should I have when upgrading to a blu ray player? Can you help me understand this upscaling thing?

I’m starting to explore options for upgrading to a blu ray player. Instead of re-buying all my movies in blu ray format, I’m coming to understand that players can have upscaling technology that will make standard movies look closer to HD. Do I have to look for specific players that have this feature? or do all blu ray players do this? Do some players do this better than others?

If you have… when you upgraded to blu ray did you re-buy your movies in blu ray?