I would stay away from the point and shoot cameras. They my work well for snap shots posted to the web but if you ever want to do more your basically out of luck. More pretty much includes printing.
I suggest a basic DSLR with a basic kit lens. Should run you mid $400 to low $500 range.
I have a Nikon D40 6.1, GREAT Camera. When I'm feeling lazy I set it to AUTO and it's a darned good Point and Shoot. I rarely feel lazy, though. I usually use my lenses that are 20 to 30+ years old. It means I have to manually focus and expose but, Hey, I'm old school, plus the camera has tools built in that help me get it right even when using my old manual lenses.
To those who grew up with film, shoot and review is super cool.
Some issues that have been brought up:
Batteries. Many cameras use proprietary batteries that can cost an arm and leg. On sale I can get a battery for the D40 for $50~$60. BUT I mail ordered a higher capacity battery for $20.
Storage: Some cameras use storage thats costly. I like the SD card. A 2 gig card that holds over 200 pictures in RAW format cost me $18. It's not the fastest card, but a fast card is only needed when shooting continuous frames.
Image stabilization: My Mavica had a stabilization feature, I didn't much care for it. The picture sort of floated around in the viewfinder. I have a slew of tripods. Come to think of it I shoot about everything from a tripod.
MENUS Don't let the menus freak you out. No matter what camera you get whether it's a cheap point and shoot or $2000 camera body the menus are going to be scary. And Confusing. After a while they are no big deal.
Software
Oh Boy ....
The camera should come with basic image editing software. It's usually junk.
You don't need fancy and expensive software, So many people get a digital then get talked into thinking they need Photoshop ... No.
Gimps free(?), I use PaintShopPro X, got it for $40 out of the bargain bin.
I should post some pictures ... Oops, its 0300. Not tonight.