Don't play by yourself. I have a few friends who are professionals in the field and even they miss sometimes. Some people devote their entire lives to studying the market and beta coefficients and a whole $hitload of other stuff and the stock can still tank or not go where predicted...
There are so many variables within every single company you invest in that it really is like gambling. If you see a hot tip on MSN money or MadMoney or anywhere else, chances are that 10 million other people already know about it and they too are going to invest. Even if you worked for a large company like IBM or something, there are tons of internal company things that you would never be aware of when it came to investing in the stock.
If you are going to just do it to play, I use Scottrade, cheap rates and good to great service. If you are serious about a long term investment, go with a professional who is not paid on commission

(Sorry CobraGuy, don't know how you are paid

), go with someone who is paid on the growth of the portfolio or even better charges a flat rate (reasonable, flat rate I would add).
It seems like you should just be able to dump $10,000 in one day and wake up a millionaire the next morning, but chances of that happening are sooooo slim and when it does they are highly publicized, so just approach with a logical head of what could happen...
Good luck!