An upright wheel is the best wheel since they offer the natural running pattern!Flying saucers are only really good as an extra toy anyways since they cause side arching and actually even the large ones don't necessarily offer proper space for Syrians to run
A 12 inch wheel is best,or around 30.5 cm.A DIY bucket wheel might be possible but it isn't always easy to find one which has the right internal diameter,and it's pretty much impossible to find a 12 inch wooden wheel from what I've seen so that probably isn't an option either.
A good option would be the Exotic Nutrition Silent Runner wheel,since it comes in a 12 inch size with a very durable stand and also comes in a color selection which is otherwise very boring but the 12 inch wide Silent Runner is green which does fit in nicely with the theme
This wheel actually has an excellent reputation among the community from what I've seen as well,which is an extra bonus.