How to update PSP firmware Via Storage Media

From this Gamespot article

The PSP-3000 plays the same games and offers the same media support as the older PSP models

So all the games are backwards compatible.

From Wikipedia

the PSP-3000 ... has an improved LCD screen with an increased color range, five times the contrast ratio, half the pixel response time to reduce ghosting and blurring effects, a new sub-pixel structure, a microphone, a new disc tray design, new button designs and logos, and anti-reflective technology to improve outdoor playability. It can also output all games by component or composite using the video out cable.[77]

So it's better. The biggest improvements seem to be the reduced ghosting (which still exists but is well, reduced) and the anti-reflective technology.

What type of encryption do you have on your router? PSPs may not support newer encryption protocols (WPA2). If use an older protocol like WEP or WPA, you may have better luck.

Edit After some quick googling, I found this article which may provide some insight. It seems WPA2/AES doesn't work, but you can use WPA2/TKIP-AES. Check your router's administration settings and you should find an option to change this.