To know which unicycle is right, we must start with the intended use. You mentioned a circus school situation; if it’s focused on that, 20" would be better. If there is an end goal of performing at some point, she will want a uni that gets her more wheel turns within a limited space.
But that might be more of a long term goal, that she can worry about later. 24" is also a fine size to learn on, even at 5’-2". The “Universe” uni you described sounds suspiciously like a UniVega, of which I have two examples hanging in my garage. That is essentially a Miyata with different stickers, and possibly with reversed colors on the seat. That was top of the line back in the day, and a very nice machine even if it needs a new tire.
If the seat has steel bumpers it’s an older one, and that seat’s not so great, but if it has plastic bumpers, that’s a better (and slightly newer) one.
Fitting shouldn’t be much of an issue; if it is indeed a UniVega, it may or may not have an extension tube in the seatpost. The proper height for starting out is to have the top of the seat reach roughly to your navel. If you don’t have hands-on with it, ask the seller for that dimension.
For parts, you may have to look around if you need a seat extension post, but if you want to replace a seat you have lots to choose from at Unicycle.com or elsewhere. Same goes for pedals. Tires can be found anywhere you can get 24x1.75 tires. The one thing to be careful of if it’s the UniVega is to not over-tighten the bearing holder bolts; they’re a little thin. This is only a thing if you’re changing the tire. Use a 10mm socket and just don’t over-tighten. We used to beat the hell out of them and I ended up drilling out the holes and putting in fatter bolts (which Miyata later copied).
Best tire will be anything that fits, without too aggressive of a tread. I just looked on Unicycle.com and was surprised to see only two offerings at 24", both of which are too fat to fit. But your local bike shop, or even department store will have something. The stock pedals will be fine for learning; once she starts doing tricks you might want to think about something with more grip, or if it’s indoor riding, something more floor-friendly.
For safety gear I’d concentrate on protecting the hands/wrists and knees first. Heads aren’t so much at risk in unicycling, but putting one on isn’t going to hurt. I bought my first helmet about 10 years after I learned to ride, and I bought it for my bike.