"Are new Friars expected to petition to join an order?"
"expected?" No, I don't think so.

"...encouraged to consider?"
Well, yes, but that consideration should begin with an careful assessment of ones skills, available time, etc - - after which, if the Brother indeed concludes that s/he should petition to "join an order," I believe the gods will consider the needs of the Monastery; the adequacy of the Monks skills; and the promise the Monk has shown by prior deeds (nodes, considerations, attitude, among others).

(re the 3 questions in your last para)
It depends! (but re the last, see above.
"be most useful?" That may be best decided by you.

And, some random NON-authoritative thoughts:

• re janitors: Theirs is a responsibility that demands a very broad and deep understanding and appreciation of the standards (and local mores) which guide them (See How do I use the power of consideration responsibly? for an introduction) ... and, since so much of the janitors work deals with markup, the preferred markup here.
• re the inactivity level of most pmdev's and re "Is the codebase really that scary?
  yep! and (IMO) yep, unless you have a very high skill level and a large amount of time to familiarize yourself with its structure.
• "largely rejected by the gods?"
  I don't think that many pmdev offerings are so much "rejected" as "non-existant" or "found wanting; tabled for further refinement."
• "The allure (is) by virtue of the orders being, well, exclusive." That's probably not a really good reason for committing to an order... nor a reason that will find favor with the Appointing Powers unless the applicant brings more than ego to the table.