How can I tell if my regulator is bad and what amp battery is needed on a Baja 150 i have been ran the quad without a battery since I've had it let it set up and now it has no spark

 

yikes! bad deal. never run a quad w/o a battery. you'll start smokin parts of which it sounds like you already have. i would be willing to bet the regulator is toast. even a dead battery is better than no battery. let me ask you this: would you run your truck or car w/o a battery? i didn't think so. a 12v system is a 12v system. one difference between truck=car and atv, is stator/alternator duties. that's one small difference.
here's a popular battery that i use in my smaller quads. if i can't use this one, i measure the battery box and get the dimensions so it'll fit but try to stay in the 120cca range, i don't go lower though, much lower.
Super Start® Power Sports GTX9BS - Battery | O'Reilly Auto Parts