If you want to get into shoot-em-ups, I highly recommend Jamestown as a starting point. At its lowest difficulty, Jamestown provides a fair challenge for novices. The game gets easier when you play with others (local-only, no online play), making it more social than your average shoot-em-up. There are multiple selectable ships, so gameplay variety is more diverse than the usual offerings in this genre.
I’m okay at shoot-em ups, and I found Jamestown to be tough during solo-play at higher difficulty settings. I think that experienced players will find some challenge here. Jamestown is kind of a cross between Dodonpachi and Mars Matrix. If you’re a fan of either game, you should look into Jamestown.
Jamestown on Steam (It’s also on GamersGate)
(I do not claim any copyright on the above screenshot)