Let me start by saying this: the roommate relationship is a two-way street. You also need to be a good roommate and that means remembering that your apartment will be this person's home, too. It's great that you take pride in your space but you will probably need to make some compromises and loosen up a little when there is another person involved. You will never find a clone of you to move in, so you need to do you best to find someone with similar values and lifestyle, set up ground rules that you both accept and then work on your patience when problems arise (as they inevitably will). That is what comes with the territory when you get help with the rent.
Now, as far as finding the right candidate, I would start with your circle of friends; it's always helpful to have the "vouch" factor. Put it out there on Facebook or at work that you have a room available and you may just avoid moving in with a complete stranger after all. Make sure to take your time and carefully interview each potential person. Talk about things like your hope for a low-key, non-partying pad and a clean environment and make sure you are both on the same page. Please don't make it into a situation where it's "your" apartment so you get to set the rules. You're a team. Also, ask for references and check them.
One more thing: even though your landlord said you can set the rent, don't try to gouge your new roommate. That's not cool and it's bad karma.