In strength training the most important exercises are the big 5 compound exercises as together they will go through most muscles in the body :
Of the 5 most important strength training exercises, 4 of them can be done using a barbell, this makes a barbell the most important equipment in strength training.
Even though a lot of barbell exercises would benefit from having different preloaded barbells (like they conveniently have in the gym), I think it is best to keep cost down buying only a single barbell with a few plates allowing different weights. In this scenario, it is probably best to start with a straight olympic barbell (the one with the thick sleeves), no EZ curling or other forms for specialized exercises - just straight allround olympic barbell. In addition I will focus on the cheapest possible instead of quality.
One of the questions to answer is how long the barbell should be : either 220 (standard), 180 or 150 (smallest) cm. I think 150 is the best as it will be more easy for the kids to handle and I imagine that it is still long enough that I can use it for all wanted exercises. While 150 cm is too short for any later training rack we may eventually buy it is for now better to focus on immediate usability and cost instead of future proofing.