16 gig is a lot of space, especially if you only have 1 gig of music. To be honest, I have about 25 gig of music on my MacBook Pro, and I have an 8-gig iPod Touch. Most of the places I go have wifi, and I never even listen to the music I have on my Touch. I listen to Pandora or Last.fm, or AOL radio, over the Web.
Now add the fact that you'll have an iPhone and that web connection will be available everywhere...you may never even listen to your own music.
As for videos, it all depends on how many you plan on loading on at a time. Once you watch one, you'll get rid of it, right? 16 gig should be plenty of space. And the apps don't take up much space at all. I've got tons of apps on my Touch, and they don't take up very much of the space.
I'm in the same boat as you, only I'm debating when I get my iPhone in July, do I go with the 16 gig, or the 8? Especially if they drop the price on the 8. If the 8gig gets cheaper, but has less features, I'll go with the one with all the features. Otherwise I don't know what to do. 8 is certainly enough right now, but I think I'd like to have 16. I'd never need more than that though. Most of my music library is crap songs that I don't listen to on a daily basis anyway, I don't have any need to have them on my phone.