I believe Navy JAG (which also includes the Marine Corp) is the most competitive. Then Army. Then Air Force. As a Navy JAG fresh out of law school, you start off as a Lieutenant Junior Grade, which is a commissioned officer. The salary ranges from $50,000 to $60,000 depending on where you accept your commission and where you're stationed (they adjust for cost of living). Also, when you are promoted in rank, your salary will increase accordingly. The only "bonuses" that you get as a law school graduate are the same loan deferment and repayment assistance benefits that all the other enlistees get. In other words, your law degree doesn't give you much leverage in getting a signing bonus.
What are the best options for military service after law school?
It is "Corps" and not "Core." HTH.
Unless you talking about the USMC, of course, in which case "Marine Core Soldier" is the correct appellation.
I'm not sure if this is supposed to be a joke
Indeed it is. Apparently I hang out on the internets too much.