[Update]: WoW Classic devs have now also addressed some of concerns about the layering system.

When WoW Classic's character creation and name reservation first launched, only a couple of servers were available in each region. This was especially painful in Europe as both of our English PvP servers ended up with constant six hour queue times due to the overflowing number of players.

In order to address this problem Blizzard soon released dozens of new servers, but due to a combination of inertion and human psychology, that did little to convince people from overpopulated servers to ditch their reserved names and start somewhere new. As such, when WoW Classic finally launched, a large amount of players continued to endure lengthy queue times in order to get into the most popular servers, all the while the rest of the medium-high servers enjoyed basically no queues at all.

To hopefully put a stop to this nonsense once and for all, as well as give players a chance to continue with the characters they already have, Blizzard has now opened up free character transfers from overpopulated servers. You can find the full list of servers at both the US forums and the EU forums.

That said, if you're on one of these overpopulated servers and you're worried about ending up on a dead server, worry not as Blizzard has already stated that even the smallest server today is biggest than the biggest server in the original World of Warcraft. So unless you really like the main menu music, swapping to a less overcrowded server is likely to be a pretty good idea. 

Whatever your decision may be, I wish you the best of luck with leveling!