Anyone correct me if I'm wrong, but since Europa Barbarorum completely revamps the factions, units, and campaign, it doesn't use anything from Barbarian Invasion. With Europa Barbarorum, the game is 50x more accurate than vanilla will ever be, leaving no reason to own BI or Alexander, unless you're a complete Total War fan. Of course you won't be able to play BI multiplayer matches, but I doubt I'd ever play vanilla multiplayer ever again.
Edit: However, if you're new to Rome, you should probably play vanilla for a little bit. The EB campaign can be pretty difficult at times. The multiplayer takes some time to master as well.