Well it really depends on what you are interested in, what kind of investor are you. Do you have capital you are willing to risk. If you lose it, will it have a huge impact on you? (losing money is never what we set up to do, but it is a reality to many new investors)
When I look for a stock I look for a few things. Mainly to see if it is undervalued. I look for stocks that are in high demand, and right now I am looking for things to buy for the long run, maybe trade along the way. There are several things that are recession proof, and there are several that are prone to shake ups in the economy. Entertainment/restaurantes/ect people tend cut back on when times are tough. People are spending more on gas, they may not go out as much ( i sure dont)
So, in picking stocks try to think about the bigger picture. Pick a sector of the market that You think will be trending up, research it. I would suggest for your first picks to do a lot of research.. Maybe make a few spread sheets and just watch the stocks you like before using real money. Pick 100 shares of a company you like and you think will do good, watch it for a week or two. Then you can see if you were right.. and if you were, good.. If not, you didn't lose any money.
many people will suggest investing several thousands when your new in index funds, or something of that nature. That is good, and carries slightly less risk.. I personally didn't do that, because i felt comfortable with the positions i was picking.. However, fund managers have a lot more information on their picks than most individual people have at hand.
Oh - and for screens.. Just pick things your interested in. Foreign, Domestic, dividend stock, non div. stock.. PE ratio. And just narrow the field down.. But dont forget to RESEARCH every play.