Emmerson,
I'd be happy to give you my two cents worth (although that's only US1.4 cents here in Australia).
If you are serious and want to a system you can grow with, I'd agree with Dale and Mark that a d-SLR system affords more flexibility, faster shooting (usually) and better image quality than an advanced compact.
A good compact like the Sony DSC-F828, Minolta A200 or such gives surprisingly good images, fast start-up, and a useful 28-200mm range in a small, lightweight, and very cost-effective system. This is a good option for travelling, is less conspicuous for street photography, and certainly not just a toy. There's a lot to like about them, although RAW performance (they take forever to get ready for a second shot, you really need to shoot in JPEG!), autofocus speed, and high ISO image quality are all compromises.
If you really would like to get serious and extend your photography (and have the budget for it), a decent little d-SLR system will be a great starting point. Please be aware that you will have to change lenses (potential lost shots and dust on the sensor), will have more to carry, be more conspicuous in a crowd, and will have a slightly steeper learning curve to make the most of it. I only really know Canon well, so sorry for the limited (er... zero) advice on other brands, but here is my ideal starter system:
-Canon Rebel XT (light, good image quality, excellent value-for-money) or 20D (heavier, better built, faster, good image quality (same as Rebel), more expensive),
-10-22mm EF-S (16-35mm equiv., only for reduced-frame sensors, expensive, good quality, but mind-blowing wide angle effects if you're not used to anything wider than 28mm),
-17-85mm EF-S image stabilised (again reduced sensor only, 28-135mm equiv. excellent range with image stabilisation, good quality),
-70-300mm image stabilised (up to 480mm equiv., good quality, image stabilised)
Remember to bring a tripod (even an inexpensive lightweight, portable one is better than nothing), spare batteries and charger, enough memory to get you by between downloads, cleaning kit, filters (esp. polariser).
Now after spending all this money on equipment, you may not have enough left over to travel, but you'll certainly be able to learn your craft. On the subject of sub $800 for the 20D, be very wary. I almost got suckered by an identical deal with that very model, and have a friend who ended up with a Japanese model, complete with kanji menu items and instruction book. She had a torrid time reurning it.
Which ever way you go, have a wonderful trip and happy shooting.
Regards,
Andrew