What is the easiest way to do that?
I'd like to keep it as simple as possible,
Easiest and simple conflict here unfortunately.
Simplest and cheapest way to do this if you don't already own suitable tools involves no powered equipment. Fair warning, it won't be the fastest, but if you get a production line going and just plug away you'll get through the sawing surprisingly quickly (one evening, easy).
Finishing off the pieces and applying a finish will likely take much much longer, but that will take a similar amount of time regardless of the cutting method used.
If you can buy the wood you need in strips of the right thickness and width all you need is some scrap wood (for sawing practice prior to cutting your main wood, and for making the jig that will allow you to do accurate repeat cuts), a sharp knife and steel rule, and one good hand saw. A clamp or two would be helpful but not vital.
If you can't buy the wood in the right dimensions you'll need some way to produce the initial strips and this is not an easy thing by hand since it's very challenging to saw with the necessary accuracy. The best power tool for doing the work is the table saw, which your comments indicate may be available. Best method may be to buy thick, wide stock and then rip long strips from the edges on the table saw.
Once you have your strips you'll make a type of bench hook or a mitre box. If you don't have clamps you can use glue or nails instead to fix a stop block that will ensure consistent piece sizes as you feed your strips into the cutting jig.
See Making a Poor Man's Mitre Box with Paul Sellers for the basic methodology used to make either jig. You just need to cut your groove in the back fence at a shallower angle than 45° but other than that you can make it exactly as shown.
Type of saw
Fine-toothed is the main thing you want here, so that the cut face requires minimal sanding or planing to finish it off.
The ideal type of saw here would be the subject of intense debate amongst woodworkers, with traditionalists saying that you should use a Western backsaw of some kind and those who have embraced the variety available to us today probably recommending a Japanese saw. Read a little more about the differences here, Comparison of Western saws and Japanese Saws
To be a little more accurate here I should say an Asian-style pull saw rather than a Japanese saw since many are not actually made in Japan and similar saws are seen all over Asia. You want one with cross-cut teeth (they will look like the smaller ones in this image, the larger, plainer, teeth at the bottom are rip teeth for cutting along the grain).
Some possibly relevant info in these previous Answers:
Are there techniques to sand small parts on a benchtop belt sander? (note Answers don't focus on using a belt sander)
Planing thin stock without the aid of bench dogs
In particular, what kind of wood should be used?
Almost anything you want. Really anything short of balsa would probably be fine, even pine or cedar which are both quite soft would work acceptably well.
But in general hardwoods will hold up to use better, arguably look better and more easily give you the contrasting colours you seek (no staining required).
A sensible combo here would be black walnut for the darker pieces and maple for the lighter ones, although there are numerous suitable choices for the lighter wood if maple is too expensive or not available, e.g. butternut, birch, sycamore, poplar, mango, ramin.