How Can I Create a Decent Website Logo?

I’ve been taking a look at a lot of eye pleasing website logos for the past few weeks. I’m trying to create a website logo using Paint.net (not gonna buy Photoshop), but the lines of my logo keep coming out jagged/pixelated. I’m using a 96 pixels/inch resolution, but things are not looking good. Is there a special way to create logos? A certain format to save them under (png, jpeg, gif, etc)?

I guess what I’m really asking is how the heck do Web designers get there logos to look so darn pretty?