Guys, first off, the new PSP model will have TV-Out, so you can play your games at home on your TV via Composite, Component, and probably S-Video I believe.

Next, if you downgrade your PSP to 1.5, you can then upgrade to version 3.5OE which is a hacked version of 3.5 enabling you to play any games that require up to version 3.5 and still play homebrew like emulators. I highly recommend it. If you need to upgrade later to a legitimate version it is possible but may be complicated and you should consult someone knowledgable on the matter.

Personally I'd recommend buying a second PSP like the new one with TV out for playing PSP games and use the older one for emulators. Atleast until hopefully the new one can be hacked.