Rake with regard to insert pocket is the angle of the insert pocket which is either negative, neutral or positive. The insert pocket dictates the type of insert that can be used, they are not interchangeable. In addition there is the insert lip/cutting edge characteristics, so those that are for lighter cutting/finishing tend to have a more positive (upward) rake. So the cutting edge angle is a function of both the inset pocket angle and the insert edge angle.
This chart from Carbide Depot gives some overall properties of the different insert shapes and general properties. There are numerous other factors that effect the application and cutting properties of the inserts. Typically diamond shapes are more fragile so used more for profiling and cutting where other inserts will not fit. As a day to day insert you are better off with a CCMT or TCMT (i.e. neutral rake holder). As far as cutting edges, it is a moot point in the realm of the hobbyist because you are not doing production levels where you will wear out the insert quickly. I can get several months of work out of an insert and typically buy them for $3-4 a piece for Iscar, Kennametal, etc. It is much more important as to getting an insert that works in your machine as far as insert characteristics and coatings for the type of turning you are doing.
Many of the insert styles like the square I use primarily for edge chamfer, others for grooving, etc. I primarily use CCMT for steel, and since I have a heavier lathe WNMG for aluminum. I use sharper positive rake inserts for boring. The DCMT is primarily for profiling and edging, but does chatter with deeper cuts.
Inserts for face mills are a totally different category so some of my inserts are octagons and have 8 cutting edges, so good for shallow cuts but not for removing a lot of material.
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