There are several things you'll want to pay attention to when selecting a server. Different servers offer wildly-different experiences, and most will have descriptions that you can read. Look for a few important details before picking a server to try:
Game type - While many servers offer the standard Minecraft gameplay, there are lots of servers with all kinds of game modes. These range from capture the flag to in-character role-playing, and everything in between. Whitelist - If a server operates a whitelist, it only accepts users that have been registered. This usually means you'll need to create an account on the server's website in order to connect. Population - This is the number of people currently playing, as well as the maximum number of people. Keep in mind that you may not actually be playing with all of these people. Servers often split large populations onto multiple servers. PvP - This stands for "Player vs. Player", and means that players can attack each other. These can be tough servers if you're new to the game. Uptime - This is how often the server is online and available. If you plan to play online a lot, you'll want to find a server with an uptime of 95% or better.