Prusa i3 MK3S. Kit if you want to DIY a bit, standalone if you don't.
I've saying this because it's a complete, stable, easy to use 3d printer from what I understand, with minimal troubleshooting/tinkering to get it to work. \Good support too from what I gather.
The catch is the price, it's in the upper end for it's spec, but you pay either in money or time.
Speaking of budget, it'd probably be possible to save quite a lot of money on silicone by using a different, cheaper material as the "core" of the toy.
As long as the surface isn't exposed, it doesn't matter if it's sterile or not, all it needs is to be sufficiently durable and flexible for your needs.
If you want it to just work and work well, the answer is Prusa Mini+ (with the optional filament sensor) or the larger Prusa i3 MK3S+. Anything cheaper and you're looking at your new hobby to be fixing and tinkering with your 3D printer.