Key criteria:
UNLOCKED GSM phone that uses at least 900MHz and 1800 MHz. These are the 2 frequencies that are widely used throughout most of the world (except in USA and Japan). (850 and 1900 are the frequencies used in the USA)
Some phones on ebay are only 1900 Mhz. Others only have 850 and 1900 MHz. These would be useless in Europe.
Still other models have 2 versions and are often mis-listed. Example: Nokia 3100 has 900, 1800, and 1900 MHz. This is/was usually sold/distributed OUTSIDE of North America. But the 3100b supports 850, 1800, and 1900 MHz. It is somewhat less useful in Europe. But it often works. But many ebayers have listed 3100b's as 3100's. So some direct questions to the sellers are required. The seller should read the exact model number off of the label that resides under the battery. Specs can be looked up on
www.phonescoop.com which only has one error that I know of.
Some European carriers do use 1800 MHz, like Orange UK, Orange France, SFR, and others. See
www.gsmworld.com for international carriers.
The UNLOCKED feature allows any carriers's sim to be allowed to work in the unlocked phone. Most GSM phones sold/distributed by Cingular or TMobile were locked to the original carrier's own sims and will NOT work with other sims unless the phone is unlocked.
The OP's V3i supports all 4 of the above frequencies so it has the potential to work in most GSM countries except Japan (2100 MHz).
Although I've unlocked many Nokia's and one ugly Moto, I have no experience with V3i's.
BTW, if the OP stays with Cingular while in Europe, unanswerd calls cost a mint since the unanswered call is forwarded BACK to the USA to the voice mailbox. So even no-answer calls to the Cingular phone can cost you a mint, too.