The best Original Xbox Box Mini device would actually just be a Xbox One S (or X)

[Pemalite]

Mr Puggsly said:

An OG Xbox device wouldn't be very impressive with lesser specs than a X1S. Especially if you wanted online features like accessing a store, improved resolutions, improved performance, etc. With that said, just push the current console for nostalgia reasons. Also, if you wanna play some classic Halo games online then Halo MCC.

Lesser specifications doesn't mean you give up access to an online store, improved resolutions, improved performance. - They're original Xbox games, they can run on a toaster.
You could take the Xbox One S chipset and almost cut it in half and it will still be more than sufficient.