With an iPhone or iPad, you can have it activated when you purchase it, buy music or apps wirelessly, add contacts, sync to MobileMe/Google/exchange, and do pretty much whatever you like.
I only connect my phone to my computer to do backups (because I don't want to lose my text messages), or to update apps >20MB (because I'm never on WiFi). You don't have to have a computer at all to use an iPhone. In fact, I have a friend who'd never sync'ed or backed up her iPhone once (and didn't know how to do it), and she used it without issues for well over a year before needing to do a backup.
I've never used Android, so I'm not sure what music store is available on the phone by default. Is it any good?