Welcome to bicycle commuting! Sorry to hear about the issues with the police, but it was a good thing for your safety. In most states, headphones are not legal while operating ANY vehicle, which includes bicycles. Invest in a good headlight and taillight, and keep them on - even during the day. "Flash mode" saves battery life and catches the eye. If you're riding in total darkness, a headlight in flash mode causes a strobe-light effect, so use your best judgment.
Cracks, seams, and potholes are a constant challenge. Depending on your size, weight, and road conditions, a "skinny tired" road bike may not be your best choice as a commuter. True, they're almost always a faster ride, but if conditions aren't optimal they can be uncomfortable and/or downright dangerous. In general, MTBs can handle rougher terrain, and when fitted with fast riding street tread ("slicks", or "semi-slicks") they make fine commuters. As a rule, wider, lower inflated tires ride better (but slower) than thinner, higher inflated tires. A little research and some trial & error, and you should be able to find a tire and inflation pressure that gives you a smooth enough and fast enough ride for whatever type of bike you ride.
Riding too close to parked cars will earn you a nice "door prize." You should be riding far enough away that if someone unexpectedly throws their door open, you won't get taken out. You have a right to use the lane when necessary, so don't be afraid to use it. Look ahead, pick a predictable line, and stick with it as best you can. Weaving around and riding like you're drunk in an effort to avoid every pavement flaw will get you in trouble. Predictable riding is safe riding. And tell your friends to back off if they're riding so close that you fear being run over.
A combination of guts, brains, and resolve is what empowers most city commuters. Look around, and you'll see just about every type of bike and rider imaginable. People tend to figure out what works best for them, and go with it. As a beginner, my best advice for you is to invest in more thinking and less spending. Be realistic about your expectations. Use Craigslist for bargain shopping. And buy a quality, comfortable helmet.
Good luck.