Is 8gb enough memory for iPhone 4s?

Would the iPhone 4s have enough memory for 20 apps 100 songs and 300 photos?

Depends on how big the apps are to be honest. If you like alot of games, then you'll need more than 8gb and if the apps are just like facebook or something, 8gb is ok. 8gb can store 300 photos and 100 songs so its okay.

Even if you add 20 large apps, you should have enough space.
An 8 megapixel picture takes up 10 to 12MB, so 300 pictures is roughly 3 to 3.5GB.
100 songs, with an average of 10MB per song, will take it up to 4.5GB.
Let's say you download 20 apps that are 150MB in size, that takes it up to 7.5GB… So you'll still have about 0.5GB for your cached files of your apps.
That's not much, but I seriously doubt all your 20 apps will be that size. The average app is just a few MB, so if you're not really into big games, you should still have plenty space for your temp/cache files to not get in trouble.
BUT, you see this can be a tight fit as well… For use and worry-free comfort, I might consider 16MB if it's not too much of a burden on your budget. It will give you plenty head room, and usually people will use more than they originally intent to (or shall I say, people don't like to clean up after themselves… A lot of junk remains on the phone that's not in use).