Other than the basic kit, the only real requirement is the base. Not sure how you'd use it otherwise.
The lower stones are needed only if you're doing heavier re-profiling, especially of harder steels. If you're just touching up, or rarely re-profiling, you don't need them.
I used the lapping pads for a while. They work well, but I found the difference is cosmetic - it didn't increase sharpness beyond the 1500 stone, that I could tell. Same with the KME translucent Arkansas stone. Moreover, if you are going to a mirror edge, and end up with a random, but very visible, scratch in the edge finish, it's just about the worst feeling in the world, and takes forever to fix
I did try off-brand strops and CBN compounds (from Gritomatic), which I think worked better than the lapping pads, but it's hard to say. Plus, with anything off-brand (not to mention the KME Arkansas stones) you need to deal with the difference in stone thickness. It sounds like it'd be easy to adjust, but getting the angle
exactly right is challenging.
I just recently picked up a KME brand kangaroo strop, but haven't tried it yet. I'm planning on trying it with green stropping compound, just for a touch-up after the 1500 grit stone, mainly just to make the edge a hair less toothy. I've given up on mirror edges. Frankly, for the cost of all the compounds, lapping pads, etc. you need to use, it's probably cheaper just to send the knife in to an expert to get to a mirror edge.