For starters, instead of looking for companies, I would start by looking for
investment strategies. As Blain stated, there are two main schools of investing: fundemental and technical analysis. Fundemental analysis involved looking at the balance sheet, the multiples, and various financial ratios compared to benchmarks or industry averages. Technical research involves studying price-volume charts, momentum, oscillators, and other methods not necessarily reliant on what the company does or its financial position.
You can learn about these various methods of investing at
www.investopedia.com,
www.investors.com,
www.stockcharts.com or by simply doing a GOOG search. While there are pages and pages of information about these two schools of stock picking (you can spend a lifetime studying it), specific questions on various aspects can be answered by forum members if needed.
Once you have your strategy in place for how you're picking stocks, you're much more equiped to screen for stocks because now you know what you're looking for. The first step, however, is to figure out your strategy.
Good luck!