There are some logistic questions for you to consider as well.

Digital or film?

For digital, how much of your budget are you going to allocate to batteries and Flash memory? Many of the recent digital compact or point and shoots have fairly accurate evaluations as to how many photos per battery (recharge) and of course per memory unit.

Since you are going to be traveling by rail alot, you may want to shoot from the train windows so that may not be the time to recharge a camera, so a second battery (if a proprietary type) may also need to be budgeted.

Are you going to carry all of your images (film or digital) with you or upload them via an Internet Cafe or send them home?

How big a camera are you willing to deal with? (Very small thin pocketable, belt pouch/pack sized, and so on).

You will probably want to consider a case or pouch for everything as well.

Consider a camera that uses easily available batteries. Power fluctuations have been known to blow out batteries while recharging. Italy, as an example, is known to have less than stellar mains in some areas and poof! there goes an expensive Lithium Ion pack and maybe even the camera while on the overnight charger.

As to specifics, I like the Canon A-series (the ones that use AA batteries), a used Canon Powershot s-50 or S-60 might be in your budget as well. These are proven tough travelers.
There are reports on some of the Kodak's not being very durable under some circumstances. Olympus makes the Stylus series which have a pretty good track record regarding moisture resistance and are very 'pocketable'. I'm mentioning some slightly older tech here as it's proven and standardized to some degree.

Hope some of this helps and if you run across a camera that grabs your fancy feel free to ask more questions.

Welcome to Photography Review and we'll all look forward to pics. You could even upload during your travels (hint hint).

Best wishes!