Congrats on your commitment to exercising! You'll be amazed at how fitness positively affects your energy levels, mood, stamina, weight loss, and body composition. Your first workout sounds great!
There's a good sticky thread on this forum about the basics of exercise: Fitness Fundamentals
To answer your specific questions:
How much you should do in a day: Start out slow, 20-30 minutes 3-5 x a week. It's important to start any exercise program moderately to avoid injury though, so don't go too hard or too fast in the beginning. Where you progress from there is up to you- listen to your body and do what feels and makes the most sense to you. It is a great ideal to do both cardio AND strength training, the former being a great fat-burner and the latter strengthening your bones and muscles as you age and lose weight (this goes for women/people of all ages, not making any reference that you are old or anything!).
What to wear: For most exercise, regular shorts, a sports bra, and t-shirt are great. If you plan on doing more intensive exercise later on down the road, investing in a good sports bra (especially if you are well-endowed) may be worth it. Sweat-wicking shirts/tank tops and/or running shorts are great if you plan to run outside or in the heat, but for moderate activity or indoor activity they aren't absolutely necessary.
Music is great, also feel free to play around with podcasts or other non-music alternatives if you want. I found I can run longer on the treadmill without getting bored if I listen to podcasts, interestingly enough!
Water- it varies from person to person how much water they intake before/during/after their exercise. If I go to a gym I keep it around and take small swigs after cardio (not during, it gives me cramps, but everyone is different) and between strength exercises. Some people don't drink any water during exercise. Just figure out what works for you and keep it balanced- you don't want to chug water and get "waterlogged" and cramp during your workout, but you also don't want to get dehydrated if you go for a long run or walk outside. Just use your common sense.
good luck and have fun!! And feel free to ask more questions, there are tons of people here who know way more than I do about exercise and are great resources for people of all levels.