Applying for university

I would suggest applying before taking a job. Granted you can do both, but you could run into a time period that will require your sim to be in two locations at the same time.

I never let my sims get a job until after they graduate.

1. They need a lot of time to study and go to classes
2. They start at a much higher level in the job once they have graduated (if it is the job that their degree applies to)

Apply whenever your sims are ready. It doesn't matter whether they have a job or not, except for its effect on scholarships. You can always quit a job if it conflicts too much with the university schedule.

The scholarships that would be affected by having a job are the needs-based scholarships, which you won't get if your sim has too much money, and Workplace Scholar, which requires reaching level 3 in a career. Your sim doesn't have to keep the job after qualifying.

I like to let my sim do odd jobs and gain experience because the gain in experience helps with getting into a distinguished degree honors program. Or just dive in with both feet.

I've yet to try this but if you want your sims to work the freelancer careers may be a feasible option. You could work whenever you want basically.

My sims work a part time job if they work at all. I know construction hours are on the weekend from 7am to 12noon Very doable.

Apply as early as you like. There is no point waiting. It often takes a day or two to get the application confirmed, and your term will not start until you decide to enroll anyway. I'm not sure if scholarships might expire if you apply way before enrolling, but I doubt it.