The subject of what compound usually has a basic answer but if you look deep into it you will find some interesting things.
First, not all are created equal. If you buy your compound at sears it will be vastly different than what you would find from leevally, handamerican, or basically any higher priced/quality compound.
I personally don't use any solid or bar compounds unless I'm using power tools. Bar type compounds are held together with a wax binder that under the friction of a power tool melts and allows even spread of the material. It can be rubbed on a strop but you usually must take additional steps to smooth it out.
Liquid, paste, and spray type compounds will usually be much more free of unnecessary materials and be more controled in abrasive size. These types are also usually geared towards knife and tool sharpening instead of surface polishing. Locally found compounds like those at sears, lowes, etc... work well on softer metals and can work with hard knife steels but results are okay at best when compared to dedicated quality compounds.
Selection of compound type/grit will depend on desired results and your finishing stone before stropping/polishing. Green compound (chromium oxide) of good quality will run around 0.5 microns (50,000 grit) and it really overkill for all but straight razors. Many use this type but rarely use it to full potential, For example, most finish a edge in the general area of 2000-4000 grit then jump straight to the 50k strop. This will work to refine a edge no doubt but fails at reaching full potential of the abrasive because it is unable to remove the much coarser scratches of previous abrasives. It would be like grinding in a edge with a 100 grit stone then trying to jump straight to a 8000 grit stone and expect it to remove those 100 grit scratches.
Selecting a compound will be a little about the steel and how polished you want it. For low alloy stainless and carbon steels I prefer a "natural" abrasive like silicon, boron carbide or chromium oxide after the use of more aggressive and higher grit diamond compounds. With new super steels and hard tool steels I like the diamond compounds, they work faster and with grits as fine as 200k a mirror polish is no problem.
Any abrasive polish will "work" but selecting the right one for your needs will work that much better.