Assuming you do paired work, do not buy the cheapest jo/bokken you can find. I've had weapons fracture on the practice floor, sometimes with splinters shed quite widely around. There is a real (small, but real) chance of injury. It is worth buying a weapon that can stand up to punishment. Also note that the fracture may not occur at the point of impact. My daughter parried one of my blows and the hilt of the bokken chipped - the opposite end from the impact and the end that is much closer to my eyeballs. For the same reason I'm skeptical of the cut down broomstick/mop handle, etc.
I agree that you don't want to go premium on your first weapon, but I would recommend that they buy something credible - the difference between the cheapest and the most useful isn't very large.
Here is an old aikido forums article on weapon materials the author is affiliated with Kingfisher woodworks, and I have purchased multiple weapons from that company. I trust kingfisher, but I have to acknowledge the bias.
Cook Ding also has an excellent article
Ellis Amdur's article on weapons
I used to covet exotic wood weapons - after reading those three articles, I'm now content with my mundane woods.
Depending on how you use your weapons there are additional considerations. I use a weapon with an Iwama style tip - The rest of my dojo uses a pointed tip. Every time someone lines up with my weapon they hold it incorrectly because they're looking for the tip. Beginner students should probably buy weapons similar to those used by the rest of the dojo.
My dojo does not use the tsuba; many of our students have to be counselled to not hold the blade of the weapon, only the hilt. The tsuba automatically corrects for that error. (I cannot remember a situation where the tsuba would have saved my fingers.). Plastic tsuba are fragile and look stupid and the retaining band is notoriously ineffective. Leather tsuba are surprisingly expensive.
When you buy a jo, buy the right length. (the shindo muso ryo jodo jo is about 4 inches shorter than an aikido jo; it doesn't make a huge difference, but if you want the student to be proficient and expect the end of the jo to be in a specific place, they need to train with the length they will use.)
One of our students has an octagonal jo - you'll see discussion of that variant elsewhere in this forum. I haven't worked with it long enough, but I don't want to work in paired practice against it - the edges are going to mar my jo.