An entry-level dSLR with two lenses, one around 18-55, then other 55-200 or 250, will be fine. At this time, the lenses should be image stabilization (Canon calls IS, Nikon calls it VR, etc), or the camera body should have stabilization (like Sony's).

If you're planning to go further in the hobby - getting more lenses, lots of accessories, etc - then don't look further than Nikon and Canon. But if you think two lenses (and probably a flash) is it, then it doesn't really matter which brand. They all take pretty good pictures. But go to a store and actually put one in your hand and try the controls.

I don't usually carry an external flash when traveling. All of the entry-level dSLRs have onboard flash, which may be used. But if you plan to take a lot of portraits on the trip, rather than just scenery, then an external flash will be preferred.