How sure is the "hired on permanently in 6 months thing?" if it is looking reasonably sure, then that might influence various decisions.
Health insurance is very important - figure that out first. It is easy to say "eh I'm young and health - why do I need this?" See some of the stories in this thread for why you need something to cover at least catastrophic health problems:
https://forum.mrmoneymustache.com/post-fire/in-case-aca-is-overturned-then-what/You may want to consider an HSA-eligible policy since you could use more tax-advantaged space at least in the short term, particularly if the position with benefits is not so certain.
You might also consider a long-term disability policy.
OK, so no 401K right now - that simplifies things a bit. Max out an IRA for sure. Find out what your interest rate is on the student loan once it starts in July - might make sense to pay that off, might make sense to keep it as long as you can. Then anything left, less your desired emergency fund and whatever you need for impending business, you put into taxable investments.
Then you put your excess income for the rest of this year into those same taxable investments.
I'd suggest reading the stock series
https://jlcollinsnh.com/stock-series/ - if you stick to a simple portfolio from the start, you'll do better than most.
And that thing you said was confusing is just saying "there are situations where you might prioritize maxing the 401K (normally 5) before maxing the IRA (normally 4). As you learn more about taxes and such, you'll probably have a pretty good idea if you're getting close to needing to do that. Hopefully by then, you're making so much that maxing both the 401K and the IRA is easy and it is a pure hypothetical as to which to do first.