Just click the job name if it's green and you're automatically promoted. To pick a different employer you have to quit first.
Zen has already told us that she is reworking the jobs system, and the current one is obsolete, so don't put much thought into it.
However if you're still interested, use this link to see what jobs get you:
http://log.ikarsoft.com/snipsnap/space/A...Lands/Jobs
The gains in the battle stats that jobs give you are insignificant. For example, if you get 0.2 per day in accuracy, and you need 500 point to upgrade a level, you'll need 8 years to do it. The gains in endurance and intelligence are good for lower levels. although school gets you better numbers. After that you'll need to donate.
One thing you might aim for is work experience. It's very hard to amass and you need a lot for higher paying jobs. Try to have a job with 0.9 or 1.0 work exp gain per day. It'll help you later on to get the nice jobs in the police department.