I'm assuming from your initial post you are not interested in funds, etc., but are interested in learning how to trade infividual stocks with some spare cash. I've been doing this for years, and it has been quite rewarding.
The bottom line is, your question is a huge one without a single answer. Trading styles are as varied as the people doing the trading, and what works for me likely won't work for you. There's just way too much psychology involved for one size to fit all. You'll have to do a lot of reading, studying and getting your arse royally kicked in to find your fit. Are you a day trader? A swing trader? A trend trader? A breakout trader? Is this all voodoo and you need to do fundamental analysis? Something else? What out of all the information available to you are you going to use to make buy/sell decisions once you've settled on a plan of action? How much time can you spend on scanning charts, researching earnings reports, etc.? You'll figure this out along the way. This is far, far from the "get rich quick" plan they promise on late night television, but it's fun
I've read just about one million books and web sites on the subject. The one constant is there is good and bad in just about every source of information (and "good" and "bad" is also often subjective). My advice would be to go to a book store and pick up a book or two that look interesting, probably focusing on how the market works to start, moving towards explanations of the different trading styles next. Check out web sites such as Clearstation.com. Then, once you've gained some level of knowledge about what you're going to do (assuming you haven't lost interest), take some fun money and dive in. Paper trading is probably a good idea for a short time just to see how the whole thing works, but is fairly emotionless. You'll need some skin in the game to make real progress. Learning to lose your own money is a big part of the game.
As for brokers, Scottrade is fine. I dumped them after trading side-by-side with Schwab and getting horrible fills, but that won't be a huge issue for you at this point. The price is right.
If you start with $1K, consider it tuition for your first semester and kiss it goodbye. Maybe you won't lose it, but maybe you will. If you can't stomach the thought of losing it, learning to trade stocks is the wrong choice at this time, plain and simple. In my opinion, $1K is really too small of a bankroll to make a real go of it, but you can at least see how it feels to "win and lose" on a daily basis. You'll have to stick to very small stock prices.
Good Luck