I don't think you can go wrong with the LX5. It gives extensive control over camera parameters and conversely, you can set it on automatic and let it do the thinking, with good results. If you go that route, consider adding the optional EVF at some point--it will be a big help shooting in sunlight.
There are competing Canons (S95, G12), Nikons (P7000) and Ricohs (GX series) in this category, and all have their fans. The G12 and P7000 are relatively large and heavy, though, while the S95 is quite teeny.
The camera will come with editing software--probably Silkypix fir the LX5--which should support basic to intermediate editing as well as handling RAW conversion. If you find yourself wanting more, you can always get a more advanced editing program down the road. Even the free MS and Apple editors aren't bad.
I don't know Gimp so can't comment on it. I started using Lightroom this year because I needed the database capabilities, but now use it for 80% of my image editing (especially with V3). More complex editing still goes to Photoshop, but it is overkill for 90% of photographers' needs. Adobe Elements is worth a look at a much lower price. FWIW you can free-trial Adobe software for 30 days and if you happen to be in school, or a teacher, the student pricing is great.