Hmmm . . . Platforms under 180 are generally RTF for a reason . . . but they're also safe as houses. Getting kits below that is hard to find and expensive since it's becoming specialized gear -- you can pick up brushless 250 kits to assemble for less . . . but safe? Depends. Lethal, no. Minor cuts and bruises, yes. Major cuts . . . possibly.
If you're just looking for a universal platform that's cheap and teaches flying skills, hard to beat a nanoQX. after that, the Hubsan 107L's are a good go-to, but they lack the ability to turn off the self level -- something you want when moving up in piloting skill.
If you want to do both configuration/building and flying . . . then there are a few 250 kits in the $100 range. They generally lack the radio gear (including FPV) and batteries at that price, but some of the kits in that range have the raw parts you need. Keep in mind most will require soldering as a staple of assembly. My beater quad was built up with the FPV260 Kit from "
MyRCMart" -- mostly RCX parts, which are fair but not fantastic. beauty of this kit: fully flexible -- reprogram or swap out the control board, flash the ESCs, replace the motors . . . all easy mods. Only downside, you wait on the slowboat to deliver
Edit: Quick look shows they do have kits with radios for +$60 . . . Wakera. Not the best, but they aren't bad either.
Keep in mind, Brushless 250's are marginally acceptable for flying "indoors" (meaning school gymnasiums -- they eat up space FAST).
Now for short courses . . . I expect you mean LoS for the near term? FWIW, threading the needle is easy given one thing . . . you're looking through the hole on the needle. beyond that, elevation is easy to guess, but depth is not -- after a few feet it becomes VERY bad. Hoops are a great idea, and I'd mount them in PVC T-junctions that way you can swap out the pipe between it and the base to change it's elevation on the fly. on an easy run, they'd all be lined up, on a harder one, you can get them vertically slaloming through.
To start, I'd recommend a triangle shaped course with the pilot just behind one vertex. from that position they should be able to see through the needle on two of the three legs, and on the far leg, have a simple pole they need to pass behind . . . perhaps a pair with a banner to set the altitude they pass on. the idea is the hoops are small, but easy to judge, the poles are easy to fly, but hard to judge.
With a bit of inventiveness this kind of see through the needle strategy can be expanded to far more complex courses . . . but simple is a good start
And FPV . . . if you go there, only do so after LoS is fully conquered, but the course possibilities open up there.