The first things you should do after buying a psp.
If you're a DS fan, for goodness sake, go and trade it on one. I mean, whats the point in having a PSP if your not even going to use it? Hello?
Turn it on, and follow the setup instructions which include time, date, nickname and some other stuff I think.
Format your memory stick. Yes, I know lose all your files. But if you do this first, before playing any games, putting music, photos etc on your PSP, your life will be a whole lot easier. Trust me.
Register your PSP on the Playstation website. Make sure to register it on your countries website.
Update your PSP. If you don't have wireless Internet or a USB cord (or a memory stick adaptor) then just skip this step. Otherwise either:
Go to settings (in your home menu), then USB connection. Then connect you USB cord and download from the playstation website and save it to the game folder under Update, then the file. The address should look something like this: E:PSPGAMEUPDATE then your file should be in there.
Go to Settings, then to Network update (right up the top) then connect or make a new connection and it will download the update.
After both of these, go to Game (in the home screen on your PSP), then down to the solid white memory card, press (X) and then the update should appear. Press (X) and then follow the on screen instructions.
Customize your PSP. This includes changing the theme, which is found in the settings menu on the main screen of the PSP. Here, you can change the colour of the menus and if you want a display picture or a theme Wallpaper/Background.
I think that this is all that you can really do when you first buy you PSP, before you play any games on it. Next you could add Music, Videos and Photos or Pictures you have made of taken yourself, of downloaded from websites and play games (Duh).