What are the different Different kinds of touring kickstands and what are their advantages?

I am using a sturdy 2nd-hand-bought diamond-framed Crescent Sport bike which I like to use for random touring. I have a middle annoying kickstand, problems described below with loading groceries and cleaning chain.

Neil's proposal in the comments, here, raised my interest to solve my problems with heavy-item-loading like groceries and cleaning chain fast. It was hard for me to see them as problems before I encountered:

Neil tried to summarize the stands but he wisely acknowledge a limitation: there are probably many and even different subtypes of which it can be hard for a person to know, perfect question for us to solve together. Please, state the stand and then its advantages. Notice the restrictions of my bike.

  Neil's explanation about the stands:

A click-stand isn't attached to the bike permanently. You'd know it if you had one. Kick-stands come in a few different varieties: One legged, two-legged (and there are subtypes in there), ones that attach to the front of the chainstay, ones that attach in back, and probably even more types I'm not aware of.

I think I live in the same uncertainty as Neil: "probably even more types I'm not aware of". I feel the kickstand that allows pedals to move freely and offers good support is a solution but which one and of which type? Please, state the stand and then its advantages. Notice the restrictions of my bike.