Specifically, I’m wondering about things I should look for, potential red flags, and tips for transport.

Congrats, Funhouse is awesome. I'm sure you'll be excited, but take it slow setting up the first time and don't get pissed if something's not working when you play the first time (easier said than done cough). In my experience, about 25% of the time something won't be working right when you set up a new pin. All that distance traveled, a lot of opportunity for something to shake loose. Ask here for advice if you have a problem.

Not sure how much you know about setting up, so here's a few tips.

With the table standing on one end and the backboard still fastened to the table, put the front legs on. Then lower the front side down so the legs touch the ground, lift the back end onto something sturdy and secure like a metal stool, couch arm, etc. and put the back legs on.

Don't cut off the plastic wrap or the strap holding the backboard fastened to the body until the table is upright with legs (I did that once, derp).

When standing the backbox up, it needs to be secured upright in place, and I'm forgetting how Funhouse does it, I think it's clips on the back. But it might be a screw inside the backbox.

Most people (like 95%) hang the key to the backglass on those little wire hooks inside the coin door.