As a longtime high school umpire, I'm going to tell you it would be extremely foolish to throw to third. If you're consistently accurate enough to get the ball over there, you're good enough to get it to second to start a double play. Too many times have I seen balls thrown out of play from first to third. Now you have one run in, a runner on third, and a runner on second, with nobody out on the play.
Even if you don't turn the double play by throwing to second, you'll have the force out there for the second out of the inning and a force play in effect at second for the third out of the inning.
And if you can't throw to second for the force there to start a double play? Well, if you can't make a good throw there, what makes you think you can make a better throw across the diamond?
If you field the batted ball within a step of first, tag the bag and then throw to second. Be sure to let the teammate covering second know he must tag the runner.
If you have to take more than a step to reach first, throw to second and get your fanny over to first for the return throw. If you're too far off first when you field the batted ball, your pitcher should be running over to take the return throw to first. The pitcher's covering first to receive a return throw on a double play is something your coach will most likely go over in regular practices, not tryouts.
When throwing to second, throw to the bag. Don't try to throw to the second baseman's or shortstop's glove. If they do their job right, they'll catch the ball. If not and your throw is to the bag, you did all you could do. Don't try to hit a moving target.