When doing certain types of inlay with wood and other material, it is BEST if your veneer or inlay material matches your inlay cuts in kerf width EXACTLY. Otherwise, you get a gap or your blank will appear to "bend" at that point, due to the extra width of the veneer or inlay material.
Making your own veneers is only going to be viable if you are either making a very small amount or making it out of a piece of exotic wood that would be a prohibitive cost to obtain as a veneer otherwise...
It's typically going to be quite expensive and hard to handle, involving a lot of time that would normally be done doing other things...
That having been said, if you have the proper jigs and tools, it doesn't need to cost you an arm and a leg for just a little bit!
#1: Dust Collector .... you're going to need some kind of protection from airborne dust.
#2: Band Saw with a Fence .... for resaw of your woods to obtain the rough veneer. You need to be able to cut reliably straight! The band saw will serve to get you close .... a "ballpark" rough cut.
#3: Planer or flat work Belt Sander ... this is to prep the blank on one or both sides BEFORE cutting the rough veneer.
#3: Thickness Sander .... If you don't have your own, or one that can handle pieces this light and small, you can easily make a small jig to handle small pieces of veneer stock. This is to finish the other side of the veneer and get it to your final thickness of choice.
Also ... if you can't seem to make the proper cuts on the bandsaw and still want to try to make veneers, and are willing to sacrifice a little extra wood to get there, a table saw with a fine cutting plywood blade or similar will work in it's place. Just make certain that you are using a riving knife behind the blade, a zero clearance insert, a properly set and adjusted fence, and possibly a sacrificial push-stick or push-block.
Now ... once you have your oversized veneer stock, you have to get it down to the thickness you need.
I've seen and replicated drawings of a fairly simple thickness sander here on IAP that is designed to be attached to a drill press. A false table is laid down on the drill press table, with 1 adjustable fence and 1 stationary fence, or if you only plan to create one size of veneer, 2 stationary fences are fine so long as you always rough cut your veneer the same size all the time.
The stock needs to pass the drum against it's rotation, to ensure it won't just be shooting out the other side.
The drum will have the sandpaper glued or attached to it's surface ... you can easily create such a drum yourself using the lathe. In fact, it's probably a great idea to make multiple drums, each with the same size but carrying various different grits.
Some veneers will be fine with 180 or 220 grit, while others may benefit best from going all the way up to 1200 grit. (I can cite a specific example of that particular wood.) Typically, you'll want grits ranging from 120 for fast roughing work up to around 600 for ultra-fine finish.
Make certain your fence is adjusted to the drum to achieve the thickness you need, and you may want to practice with a piece of cheaper wood to get to the thickness you are looking for ... then lock the table down by clamping it to the drill press table and pass your veneers through the drum sanding attachment one by one till you are finished.
It is typically best to make 30% more than you think you'll need, to cover for breakage in handling or damage/loss during use, and in case repairs are required it's best to have a little extra on hand.