Hello friend!
I've been a bike messenger for two years and I've ridden a few bikes around urban areas and everything has it's pros and cons. I'm on a bike about 7 hours a day, Monday through Thursday just for work. There are a lot of opinions as to what you need or how to get started, but I'm going to try and help out with as non biased as possible guide for anyone trying to get into cycling.
First what you will need
1. A Bike (duh)
2. A Helmet
3. Front and Rear lights
4. Lock(s)
Honestly that's it. The lights are for riding at night but in some states it is the law and depending on wear you live cops can be a pain about this. Anything else is totally extra. Kits, shoes, clips, clipless, carbon, bags, etc. ALL EXTRA. You should be riding in and on what you are comfortable. I've spent way too much money on kit and I never use any of it. But lots of questions get asked about bikes and I'll try and answer some common ones. One thing to keep in mind is where you live and where you're riding. Living in a rural area would basically rule out buying road bikes or riding to work in work clothes. The climate and the geography can greatly effect how you will determine what to buy.
What kind of bike do I need?
Whatever bike you want! Make sure you set a budget for yourself that is reasonable. Like most things don't go too cheap and don't spend your life savings on this. A good starting point for a used bike (if you're a REAL beginner) is about $80-120. I don't recommend going with one of the $100 new bikes from walmart or target mostly because they don't last. I've had these and worked with enough people who've bought these and they simply fall apart in an unreasonable amount of time. As prices go up, weight goes down and reliablity goes up. Simple as that.
There are so many kinds of bikes, where do I start?
If you want to go with a mountain bike get one! Fixed gear? DO IT! Find the bike you want this is important as riding a bike you enjoy will keep you riding. However everything has its pros and cons just like everything else. Mountain bikes are rugged, durable and can go almost any surface you encounter. They're also heavy and usually have more parts involved with suspension being in the forks and sometimes in the frame. The tires are also not as readily available when compared to road and commuter bikes.
Road Bikes are becoming the new norm. They are super light and usually very fast. They are also available from the low hundreds to tens of thousands of dollars. They do tend to break down more often, but luckily replacement parts are in great supply.
Next would be single speed/fixed/commuter. These are the easiest bikes to deal with. Little to no maintenance required and can take a beating, but are sometimes the hardest to ride as you don't have gears to help with hills. So depending on your physical ability and the area this can be a make or break on single speed/fixed.
There's a couple other types of bikes but most of them are really just variants of the ones listed.
What clothing should I wear?
You need what you're comfortable riding in. Helmets obviously. A lot of people are ok riding to work in a suit and tie. Others would die from that. Go for a ride to work/school when you're off in what you would normally wear if you drove. If you feel you're getting too hot or too cold then it's time to maybe invest in clothing and a bag. You can buy cycling specific gear or just improvise. For carrying stuff backpacks are fine, but laptop bags are not. Not unless they have a T Strap. This will secure the bag with a buckle that goes around your side and can be added to any style of laptop/messenger bag cheaply and easily. Proper cycling messenger bags will have these but usually exceed $100. Lots of people like kits, or the skin tight shirts and shorts lots of cyclists wear, but I think they are insanely uncomfortable. They do include pockets in the back which can be helpful for tubes, snacks and water bottles. Some people like jeans or shorts and some people like full workout attire. Always make yourself comfortable riding your bike.
Do I need gear or spare parts?
It's never a bad idea to have spare tubes. The right size will be indicated on your tire. Should look like 700x23 for road or 27.5x2.0 for mountain bikes. There can be some variances in those numbers but those are fairly common sizes. A multi tool with allen keys, phillips and flat head screw drivers and a 15mm wrench. Then a small bottle of chain lube. These aren't too heavy to carry around in a backpack compared to most laptops, binders, and books.
What are the rules of the road?
Real simple. You are basically a car. Always check your state bike laws if you're unsure. Just remember the same rules as though you were driving. Don't blow past stop signs and redlights because you can get a ticket on a bike. Just remember to signal which way you are turning or changing lanes. Just point by the way non of that dumb arm hooking stuff. Going right? Point right with your right hand. Same with left. If you live in a bike friendly area cars usually aren't too terrible. If you're not so fortunate they will hate you and want you off the road. Don't pay attention to them. You are allowed to be there and don't let others discourage you. Own the lane and you will be fine. It's polite to move as far right as you can safely to let cars pass but you are under no legal obligation to do so (again check your bike laws). Just don't do anything you wouldn't do in a car and you'll be gold.
There are so many different parts at my bike shop what's the best???
Look, assuming your bike shop isn't run by Specialized bike vendors they will probably help you out as long as you're honest with them. Don't go in trying to impress anyone. They won't be. If you just learned how to ride, let them know. They're not going to sell you a $75 Carbon bottlecage when you need a $5 one to hold your gatorade. They won't put you in cycling shoes with SPD-SL cleats if you aren't ready. If you aren't sure about anything just ask.. No one is out to get you or your wallet.
If you're serious about riding there's a world of stuff to get into. It's pretty great riding around cities, suburbs and trails. Find some group rides and meet up people to go on weekend rides. Ride to work or school. Ride to the grocery store. You'll start feeling better and get more confident on the road faster than you'd expect. Make friends with people in bike shops. They'll teach you a lot and as long as you're not a pompous ass about you and your bike they'll probably help you out even financially. It's not as scary as some people think it is, and if you just want to ride it's super simple to get road ready these days.
Good luck and great riding!!!