My favorite type of server is a server based on one thing and one thing only. By that I mean I don't like servers that have a hub with multiple different servers connected to it (I.E. servers like Mineplex, Hypixel, and DesiredCraft). I also don't like factions/PvP servers because I'm horrible at PvP, so I guess you could say I'm pretty picky when it comes to choosing servers.
Factions has been my favorite type of server for a long time, creative at a close second. The problem with factions is that they were only really good during 1.5 and earlier. They all seemed to go downhill MAJORLY after 1.6, and that saddens me. If I found a really good one that was able to capture what was so fun about the 1.5 servers that are now dead, I'd play it to near death.