You actually don't need a PS3 to play the PSP3000 on a TV, you just need the video out cable (hooks into the miniUSB connector on top).
You can hack your PSP pretty easily these days, enabling you to run emulators and lots of homebrew.
PS3 link lets you swap PSone titles from the PS Store between PSP and PS3. There is a growing library of classic PSone titles you can purchase straight from your PSP, through your PS3, or on your PC that are playable on the PSP. Unfortunately, the PS store is kind of clunky...but it has improved a lot lately.You can also access media from your PS3 remotely (via wireless internet) through the PSP, so if you have movies, etc. store on a PS3, all of that can be streamed to the PSP on the go as long as you have wireless access.
The PSP browser is meh. The text entry systems are clunky, making it tedious to use. But all it requires is a wireless connection. The DSi's browser is much better thanks to the touch screen.
Go get God of War: Chains of Olympus and LocoRoco 1 and 2.
http://pspslimhacks.com/Tons of info on the PSP and what you can do with it.