To my knowledge there is not just a single device that does everything you want and meets all your requirements.
The IPOD Touch doesn't have a microphone by default so it wouldn't record for you. It also doesn't have an FM Tuner. Though if you have a wifi connection you can use the IHEARTRADIO application to connect to most of your favorite stations. Ditto for an IPHONE which has a 3G data connection. Honestly you might want to look at an IPHONE. If you want to browse sites, download from those sites, and be able to take this around to plug in at friends that is the way to go. It also has applications up the wazoo, it doubles as an mp3 player, you can find an application to record sound (though I dont know how great it is) and a whole other mess of features. You always have your cell phone on you so you might as well roll this other device into it. Or of course you can use an Android Based phone, it will do the same things, similar apps for what you want to do if you don't want to deal with at&t.
An ITOUCH will do most of what you want but if you dont have wifi no FM radio and no downloading off sites.
