360 magnum or LA?

I think you have already answered you own question.

If I had to start from scratch, which is the better engine to spend my money on for say an mid 10 second A body, the LA or the magnum?[/QUOTE]

IQ52 was correct until you said mid 10's on a budget. I know "tight budget" means different things to different people, but.....
You're probably better off building a 4" arm stroked 340/360 LA and using some well prepped J heads or some Eddies to get to that point. Not to mention the converter and chassis prep it takes to run those numbers. You might look into a forged rotator and a 200 shot if there is really a tight budget.