You most certainly can! It all depends on how powerful your PC is. Of course, the more instances of EQ you run and the more player you have on the server, the more likely you are to have stability issues.
But, if you are only planning to run 1 instance of EQ (not multi boxing) and just a few players, you shouldn't have any issues.
Unless you are planning to do something specific, you probably don't even need to run your own server. There are plenty out there already to mess around on.
You can find a nice list of servers and their descriptions here:
http://www.eqemulator.net/forums/showthread.php?t=24875
Setting up your own server is pretty easy. But customizing it or adding content is the hard part. If you want to play something like live, you would probably want to play on The Grand Creation. If you are looking for something different, there are many custom servers out there. You can normally see which ones are good by looking at how many players are on the server from the server list.
If you just want something private for your and your friends, then setting up a server with the standard AX or PEQ database should do just fine.
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