A quick update.
I chose not to buy the ultra-cheap stepper motors (5-wired) but 4-wired stepper motors which can be controlled by the easydriver V 2.0 board. The reason is that apparently the easydriver provides more flexibility and can possibly be re-used in another project. Here's my shopping list, I hope the parts will work well together. I already placed the order.
As for the chassis, I think I will make a custom one based on this layout but bigger.