All of the major brokers are legit. They wouldn't be in business long if they "run off with your initial investment."
Most markets trade 24 hrs a day now, and almost all of the major trading platforms can be programmed. Most of the commission fees are similar, so pick a platform and broker that meets your needs, your style, your time frame.
Trade a simulator at Investopedia while you learn and save your money.
Getting Started In Stocks
http://www.investopedia.com/articles/bas...
Five Minute Investing: How To Evaluate A Trading Strategy
http://www.investopedia.com/university/f...
The Cardinal Sin Of Beginning Investing -- And How To Avoid It
http://www.investopedia.com/stock-analys...
Read a good book or three, like Investing For Dummies, available at your local library for free.
http://www.investopedia.com/university/b...
http://yourportfolio101.com/index.html/l...
http://www.howthemarketworks.com./
http://stockmarket.makemoneyideas.in/
http://beginnersinvest.about.com/od/inve...
http://www.fool.com/School.htm
If you are just getting started, I would suggest that you go to a Charles Schwab office and talk to them. That's how I got started about 20 years ago.
TD Ameritrade (tdameritrade.com) You don't even have to trade with real money, you can do a fake account to get your feet wet.
I've been thinking about toying around with some online trading but I don't really know much about it.
I've also read that there are computer programs you can use to continue trading while you're away from the computer.
Is anyone currently doing this and has anyone found a legit computer program that I can run at night?
I know a lot of them are scams and people just ready to run off with your initial investment and profits so I'm a bit dubious to just kinda dive in and try stuff out like I usually do when I want to learn something new.