It's a decision only you can make, and the reality is that either guitar will likely serve you well. I always recommend the Strat as a first electric - seems to me that it is more versatile and I find easier to play. Body width and weight being an issue on the LP, and for me the position of the controls as well...

Give the strat a chance, and for that matter try every guitar you can afford to help you make an informed decision. When you do decide on the type and manufacturer, make sure to play every one of that guitar the store has - each one will be slightly different. Make sure you get the sweetest one...

And welcome to GT... :)