According to T-Mobile's site, You'll be able to use your phone in Japan, South Korea and Mexico just fine, T-Mobile has a presence in Europe, so it'll work fine there too. It'll cost you an arm and a leg++ to do anything, but it will work. Check http://www.t-mobile.com/International/RoamingOverview.aspx?tp=Inl_Tab_RoamWorldwide&WT.mc_n=ILDCoverage&WT.mc_t=onsite
to see the prices of any country you want.
As for the phone, T-Mobile happens to sell the G1, which has many excellent programs for email access, and a very find physical keyboard. You can even use it as a wifi router with http://code.google.com/p/android-wifi-tether/
if you choose to check email or type on a laptop.