Welcome to the low end!
My take on your questions --
1) There are all kinds of basses, and no one of them is "the best" for anything, they all have different personalities, just like people. The best thing (canned advice here) is to go to a store and buy the one that YOU like the best. Some factors to think about:
-Looks - you should LIKE your bass. If you think it's ugly, you won't be motivated to practice.
- Feel - ask the store for a strap, see if you're comfortable with the weight and balance on your shoulder. Some basses have bad "neck dive" - they look cool hanging on the wall, but then you find yourself wrestling with it to hold the neck up all the time once it's on your shoulder. Also, some necks are wide, some are narrow, some fretboards are curved and others are flat, etc. See how comfortable it is in your hands.
- Sound - ask the store to plug it into an amp and play with it some. Do this with different basses, you'll notice they have slightly different tones. These can be varied by changing the controls on the amp and on the bass, but again, make sure you're happy with how your bass sounds.
2) strings - the main types are roundwound and flatwound. Rounds are rougher to the touch (they're like a wire wrapped around a wire) and they sound more bright and aggressive. Flats are smooth to the touch (like tape wrapped around a wire) and sounds more smooth and warm (like old school motown). To start with, just use whatever strings your bass comes with, but eventually you'll want to experiment with the strings that create the sound you have in your head. They do come in different thicknesses (gauges), which affects tone and tension some.
Small hands are not an issue with strings, but hand strength is a little bit. I'd strongly recommend asking the store to give the bass a setup and make sure the "action" is not too high - that means how much pressure is needed to press the string down to make a note on the fretboard. The main variable in action is the height of the string from the board, but things like string tension play a role too.
A lot of people say get a short-scale if you have small hands, but I'm not really persuaded. There are a lot of petite ladies out there who are rocking full-scale basses with no trouble. Unless you're crazy small you should be able to handle it. Buy a short-scale if you LIKE it, but don't feel you HAVE to because you're too small to handle a big one.
3) Tips: yes, +1 to getting a real teacher to get started with if you can afford it. If not, get a good book. Split your time between learning technique and music theory (to become a better musician) and learning songs you like (to enjoy what you're doing). Practice at least a little every day - 15 minutes a day is MUCH better than a 2-hour marathon once a week. Also - VERY important - learn good technique and posture to avoid straining your hands and wrists. Some people get themselves into carpal tunnel and tendinitis and you don't want to go there. Take a look at chriskeuken.nl, at .