What is the best soil types for agriculture?

Loess.         

Soil types are not directly related to fertility, but capacity to be fertile is strongly related to the mineralogical composition of the soils, and soils with high potential nutrient storage capacity do tend to have higher nutrient contents, so fertility is somewhat indirectly related to soil type.

Also, "fertility" depends on the needs of the target plants as much as the provisions of the soil, and drainage capacity and moisture retention capability also impact "fertility".

So, it is complicated and there is no direct ranking that can be done which is meaningful.  It is useful to know aspects (characteristics) of the soils with regard to ion-exchange capacity, drainage capability, moisture retention rates, and so on, as part of the evaluation.  In effect, the only real generalization is that the more diverse mixtures of minerals and grain sizes tend to be the most useful for agriculture.  Monomineralic sands are crappy for most plants (some actually like them though), but loams or clay loams can be very good for cultivation. Enough mud (clay, correct types of clay) to be able to chemically absorb nutrient components and release them to plants eventually, and enough fine porosity to allow for moisture retention, yet enough coarse porosity to allow for fairly rapid infiltration of water from the surface.  too much "mud" leads to hardpan, but not enough mud leads to overly dry soils.

It is a complicated enough issue that most people who study agriculture have at least one course (if not multiple courses) on soils and the ways that soils can differ, and ways that human interventions can augment or improve natural soils to make them better for agriculture, and of course the various tests one can make to define what needs a given soil likely has. I went to a state school that had such degree programs and took a few of those courses, because this geologist was interested in the subject for other reasons.

There is no "One-size-fits-all" answer, though.

In general, rain forest soils are the worst and desert soils are the best. Surprised? You shouldn't be. Which soil gets its nutrients washed away by 80+ inches of rain per year and which retains them because they get less than 10 inches per year. Think of desert soils as instant agriculture. You just have to add water.

There is no such thing.  There are infertile soils for various reasons but there is no BEST soil. You see different plants, rainfall and other factors require different soils.  Shepparton Fine Sandy Loam is great for vegetables but it doesn't hold water for long.  It needs regular spray irrigation.  Lemnos Loam is heavier.  It can be irrigated by flood irrigation.  Grasses, trees and most crops grow well. A heavy clay has the greatest nutrient.  It can withstand salt. Although it takes ages to GET wet it can hold that water right into the heat of summer.

On slopes you need a soil that doesn't wash away.  What about a soil that can withstand animals walking on it without becoming plastic? 

So you cannot ever say one soil type is the BEST soil for agriculture.

"sort it out" - in other words you want us to list all the different soil types and sort them for you based on one of 2 sources you have just as much access to.

No, I did my homework.  You do yours.