Get all the necessary state and national paperwork in as soon as possible. People from my class who passed the national registry and had their paperwork in early got their state licenses anywhere from three to 12 weeks after finishing clinicals and the exam. Just remember with a government bureaucracy, if anything can go wrong or be delayed, it may well.
My file got lost on someone's desk in the state office and was complete for three weeks before I called and a nice lady realized what had happened.
As for employment, my experience has been that for the private transport services, apply and they'll be offering you the job that afternoon. For the EMS 911 services around here, they have testing dates a number of times a year and there's sometimes a significant delay between testing and an employment start date. For either of these types of jobs, there may be a mini-academy that lasts M-F 8-5 for a couple weeks, so be cognizant of that if you're taking college classes at the same time.