I started my grandsons on Honda 50's primarily because there's no clutch to worry about and confuse them. Makes it purely a fun thing. They also have optional seats which raise the rider so they can grow into them or larger kids can ride them. Once they get that down pat and they are having lots of fun the next step up is 80cc to teach them how to change gears. Be patient because that could be a year or more dependent upon how often they are able to get out for some experience. It's important not to push them too hard or they'll not enjoy it and continue on. Once they've got the basics down they'll be hooked.
For kids that age and size there's some used bikes and plenty of PPE available. They grow fast and can need size changes more than once a year. ATGATT for the young ones is important because they'll be falling and hitting things a lot. Judging by your avatar you already know this.
Quite honeztly even used Hondas or Yamahas are insanely priced right now VS the inexpensive Chinese offerings even sold on Amazon with rave reviewz for $1100- $1600 new and 250cc. Alot of very good reviews for what youre paying for an amateur entry
Offerup you will see the new listingz galore.
Age is never enough to know what size to get, as my son and his cousin are same age and nearly 8" difference in height. My son is much larger and can handle a 125cc