Seasonal rental and/or buy equipment for the oldest and hand it down. Renting for the day is a PITA. Fill out the form, get boots that fit, adjust the bindings, head to the bathroom for the second time....you get the idea. If buying remember boys don't like pink and some girls only want it.
Most swaps don't see used gear under 100cm. It doesn't make it in the door. Gets bought out in the parking lot! But just like adult skis look for signs of abuse, check the edges, any screws missing, any parts of the bindings missing, any repairs....As for boots, take the liner out and have the kid put them on. Then you can see how much room is left. If really young, play with them like slippers. Yes you can take the liner out of those small rear-entry boots. Takes some work, and there won't be a full liner with a full back. Check the boots for missing parts, broken parts, broken plastic, broken lugs, rips in the liner, etc. I've worked too many swaps and see all kinds of crap and limited good stuff come in.
I would suggest if you buy used from a swap, wash the liners before you go skiing. Who knows what's in there.