GIMP is another good one, but requires slightly more power. It's for good reason, though. It's got some really nice extra tools that Paint.NET doesn't have. GIMP is basically a photoshop clone. It's super similar, and really nice to use.
I used Paint.NET on my laptop. It's easy, free, has a lot of useful tools, supports transparency, and is low-powered if your laptop/PC is old or slow. If there's anything else you'd like to know, go ahead and leave another comment.