Camera advice needed for non-techy beginner photographer
We want to get a new camera before we go on holiday in November.
We currently have a Kodak Easyshare Z1015 IS which comes with a 15x Zoom. It's fine. I've never really learnt all the advanced features but the one thing that irritates me is slow shutter speed. I'd like to be able to take photos without waiting ages for it to think about the last one.
I'm not a great photographer but I want to do a basic course before we go. So I'd like advice. Should we just get a compact point and shoot, which will reduce luggage? I don't know if they're any good or if the lenses are OK. I'd prefer a better lense than we currently have as I find it restrictive.
Or should we get a DSLR and learn how to use it properly? If so, what would peeps recommend and why? Can we get something good for under $500 or do we need to spend more?