Wow, new DM looking for a it of advice. Cool!

Dealing with rules issues & player conflict is part of the not-as-fun aspects pf being a DM. So, my advice on that is simple. Focus on having fun and communicate. Most problems can be solved by calm, rational communication. Don't be afraid to toss out rules, or make them up if you don't know them, in the interest of fun. However, you need to remember that the spotlight should be on the PC's. Do not ever get so attached to an NPC that you are afraid to let them die.
Now, on to your question on how to mentally prepare to DM. That is an interesting question that I have never thought of in those terms before. For me, it is mostly anticipation. I try to come up with cool NPC's, cool items, cool story devices, cool scenes, cool what have you. Something that I will enjoy playing with and can look forward to. As I go through the week, I think about how I will run that through the game. As I think about it, I might have ideas for combat tactics that I need to look up. Or, I might have a question on what skills will be relevant. I might contemplate an interesting way to build out an NPC. Not necessarily the most efficient, but the most interesting, For me, I end up thinking about this stuff a lot. I might think about while driving to and from work, at lunch, at home while posting on EN World (even while writing this post I have tried to think of what I do to prep, and a few ideas have come up), whenever the throughts hit me basically. Sometimes it is a rough week at work and I am not as prepared on game night as I would like to be. Sometimes, I am so jazzed up that I don't need to reference notes or anything. Usually, it is somewhere in between. Now, I am not suggesting that you need to be as freaky as I am about it.

But, if DM'ing is something you enjoy, you might find yourself spending more of your free time thinking about abstract game stuff.