PSP help - downloading games?

You're out of luck. There is no way to run a custom firmware on the PSP-3000 series consoles, and you need custom firmware to be able to run downloaded games. The best you can do is buy the games you want and await further developments.

To answer your other questions, in order... many PSP games are significantly smaller than 1.8GB in size, once you have them on the memory stick you can indeed run them from the main menu if you have custom firmware, and I use a 4GB SanDisk and a 4GB Sony memory stick. I have both the original model and the slimline PSP-2000 series consoles.

Jam it back in, in the dark.

Originally Posted by gaming

Just out of curiousity, where would one go to get these custom firmware?

There are various different resources for CFW and homebrew on the PSP, but none of it will work on the PSP-3000 right now, so please don't try it. You'll only risk damage to your console.

PSP Hacking & Custom Firmware - MaxConsole Forums

A forum such as that one is a good place to start, since the members have accumulated a wealth of links and information. I repeat, until you've read news from a reliable source indicating that the PSP-3000 has been hacked, don't try anything you might regret.

There's nowhere I can't reach.