Welcome to the digital world mb. I resisted the digital stampede until last Christmas. It only took a week or so to realize I liked digital and a month to realize there were things I could do with digital photography that I couldn't have done with film - at least with my film camera rig.

For basic photo editing (resizing, red-eye removal, etc), any software that come with you camera will probably do the trick. If you want to do a more than just the basics, Paint Shop Pro, as ShadesWolf said, is a good choice - it is what I use. Another program that gets good comments is Adobe Photoshop Elements. Both of these programs go for about $80-$100 (US) normally, but if you catch a sale or can use an upgrade rebate, you can get them for a much better price.

As for advise on using the camera, learn how to use the camera on its manual settings and how to make adjustments to its automatic settings to suit the situations you'll run into. This will allow you to make any adjustments if the pictures aren't coming out right on the preset automatic modes like the landscape/scenery one it sounds like you'll be using a bit.