Hi Berg,
It would be nice to address you with your christian name instead of your 'Handle'.
There is no 'Hard and Fast' rule about Mobility Scooters', the only thing I would suggest is try and find one that is working, and has decent batteries, as these are quite expensive to replace new. I would stick to a well known type personally, something like a 'Shoprider' or 'Freerider', as these are the most common, but others have used 'Sterling', but there are so many to choose from.
I have also seen 'Batricar' models advertised, these look to be a good option, but I haven't had chance to examine one as yet.
I have found from stripping three different models, that the 'Shoprider' type are 'Metric' fittings, and hubs and steering parts will interchange with others such as 'Freerider', while 'Pride' scooters use 'AF' (UNF / UNC) bolts and fittings.
I have recently been shown an old 'Town and Country' scooter, this had three large wheels, about 14 / 16 ins in diameter (around the same size as 'Toylander' models), but the interesting bit for me, was that they have just one motor which drives the rear axle via a heavy (ish) chain, and this (axle) has a small 'Differential' unit built into it.
The other thing to look for is features, such as Lights, Indicators etc, as this will add realism to the finished vehicle. Some of the scooters (shoprider, freerider) have small round lights (look at my rear lights) under the rear cover, and these are ideal for the 'Toylander'.
Try and find the cheapest option that works for you. Bodywork is unimportant as it isn't used, so this will work in your favour, as most people want a decent looking scooter for a relative.
I have seen 'Scooter Dealers' advertise on Ebay from time to time, selling off old, damaged and traded in scooters, and these go quite cheap, just bide your time, and keep your eyes open for bargains in your area.
The other thing to try is 'Telegraphing' information. Let all of you family, friends, work collegues know that you're building a 'Toylander' and ask them if they know where to find a scooter. You might just drop lucky (as I did 3 times), and have one 'donated' to you for the project!
I have sent other members messages in the past, if I see something that they are looking for, and will do the same for you (or anyone) if I see one in your general location, as the more 'eyes' you have, the better!
Hope that this helps you,
Keep Busy,
Regards,
Mark.