Are design software and wedgie sleds necessary for a basic, starter segmented project?
The design software is not necessary, simple math will tell you what your angles should be. Example: 16 segment ring - 360 / 16 = 22.5 degrees, that is the space each segment will take up in a circle and is referred to as included angle. The angle of each segment in each joint is half of the included angle or in this case 11.25 degrees. If you cut the number of segments in half to 8 the included angle becomes 45. The decimal degrees can be a pain so if you consider 360 / 12 = 30 / 2 = 15, many miter saws have positive stops at 15, 22.5, 30 & 45 degrees. The design software is primarily used to layout these elaborate designs with the 2144 pieces in them, but if you don't care for that or are just looking for a simple starting place, just go with one species.
The cutting can be done with a table saw or a miter saw, my personal preference is the miter saw, because the work piece is stationary and the saw blade is moved to make the cut so that is what I will describe. The first thing to do with any type saw is to tune it so it cuts at 90 degrees to the table and 90 degrees to the fence or cross cut guide.
This is the setup I have been using, but you can cut your segments directly on the machine table. The toggle clamp holds the segment so that it doesn't go flying or jam up between the blade and the stop. To cut without the auxiliary table or clamp you will still need a stop. The procedure is to first cut the angle on the end of the strip, then flip the strip over push it up to the stop and make the second cut = 1 segment. The procedure without the auxiliary table and clamp is to make the cut and before retracting the blade shut down the saw and wait for it to stop before retracting the blade, otherwise the segment may be damaged and or take flight.
The glue up of each ring can be done all joints at once, if the angles are accurate or you can make them in two halves with dowels in 2 joints to account for the inaccuracy. The assembly can be clamped with SS hose clamps. Note the details of gluing up rings has been discussed many times before.