I used to have a Kodak similar to yours, and actually you already can take photos of lightning, you just gotta turn the dial to 'M' manual mode, and mess around a bit, Im pretty sure you can get shutters from 1/1000 to 8s on that camera. Just mess around with the menus till you find it, it took me a long time to figure it out.
It all depends on if you're serious about Photography, if your just going to shoot lightning, use the cam you have. But if you really want something that will bring all the options to you, go with a DSLR.
I got a Nikon D40 in early march, for $500 with a 18-55mm kit lens. (great deal) Like Rob, my next lens will be a wide angle.
If your going for DSLR go with a Nikon or Canon, they have the best selection of lenses, and finest quality of glass IMO. Definately Know that it will be a huge investment though. I think it totaly worth it.
If money isnt a problem I'd go with a Nikon D40 kit or a Canon XSI Kit. If you're not sure youll be too serious, either figure out how to use yours to take lightning shots, or get an upper level point n shoot.
Hope this was helpful