Home basing: the employer buys you tickets to and from wherever they need you to report. Unlike airline commuting where youtravel space available and you are responsible for being there on time.
Corporate aviation schedules vary widely, there's no real industry standard other than the FAA rest/duty rules. Everything else about corporate varies widely as well. All depends on the employer. Highly stable, well paying corporate jobs where you are treated well are rare, and very hard to get (nobody leaves).
Type ratings are generally done in simulators, and cost anywhere from $5k to close to $100k. But contract pilots will normally need actual PIC time in the aircraft for insurance reasons. You probably can't be a successful contract pilot with only a type. You'll also need to know people... corporate is very much about who you know, so you generally have to work your way up building flight time and net working.
Pay and benefits will be better at the major airlines, in most cases much, much better. Opportunities at the airlines are quite literally at an unprecedented level right now; many corporate pilots are leaving for the airlines. If your dead set on corporate, there should be plenty of opportunities due to pilot shortages. But I'd shoot for airlines. Also as a military person you'll find airlines to be more organisational in nature, while corporate will tend to be more personality driven.