I can't speak to all servers, but some decently populated ones I am or have been on are
　○ Adamantoise
　○ Behemoth
　○ Faerie
　○ Leviathan
　○ Midgardsormr

On the legacy side most are well populated, though I only know of Sargatanas first hand. Either way just note that while you can create characters or transfer to legacy servers, you cannot transfer from them to a non-legacy at this point in time.

If you are new and worried about leveling issues, I would look specifically for a group that can help you level, and is story friendly and make your decision based on that as opposed to the overall server itself.

The biggest problem I find for new characters right now is finding a group of new players, or new player friendly via duty finder, so knowing going in that there is a group that is friendly and have the people to help you out is probably a must.

On populated servers that have a lot of people you still have to know you have a good friendly group during the leveling process, because so many of the groups right now aren't interested in story, only on leveling for end game, or doing end-game.