help me choose the Carbide Inserts that go into them, and Explain in detail why.
No one here is going to type out the contents of a week's lectures at a vocational school. So there is a serious limit to how deep "in detail" this will be. You have chosen a proprietary (Top Notch) and an actual published standard (SDJCL) toolholder.
"Top Notch Holder W0.50 L3.50" (NKLCL0805V)and a Right Hand Variant.
The Top Notch name is owned by Kennametal, and it often refers to defacto standard insert tooling of a narrow, upright profile. That is not the case for your toolholder, which takes a laydown diamond insert of proprietary design. If you refer to the Kennametal catalog, your left-hand holder takes NP..51L inserts, and your right-hand holder takes NP..51R inserts.
You probably want NPGR inserts. These inserts are available in a variety of grades (carbide body and coating materials) and chipbreaker styles. To find the specific part numbers you want, you must consult the Kennametal catalog and know A) what kind of material you are cutting, and B) whether you are roughing or finishing.
"SDJCL082 1/2" Shank" (and a Right hand Variant).
This is
industry standard nomenclature for a tool holder taking
industry standard inserts.
S means inserts are fastened to the holder by screw, so the inserts must have a countersinked central hole.
D means inserts are diamond shaped with a 55 degree narrow point.
J means the toolholder is side-cutting, with the insert presented at a -3 degree flank angle, and the head is offset from the shank.
C means inserts have a 7 degree front relief angle.
L means the toolholder is left-handed.
08 means the toolholder has a 1/2" square shank.
2 means the toolholder takes inserts sized by a 1/4" inscribed circle.
Now, if you go looking at the industry standard insert nomenclature, you will see that you want DCxy21z inserts, where
D is a diamond shaped insert with a 55 degree narrow point.
C is an insert with a 7 degree front relief angle.
x is any tolerance option
y is one of the single-sided countersunk central hole options (B, H, T, W)
2 is an insert sized by a 1/4" inscribed circle.
1 is the thickness associated with a DC..2 insert in a SDJC.082 toolholder (you learn this, it's not in the standard table).
z is the corner radius, probably 1 or 2 for this size of insert
So DCMT211 would be a very typical insert size and shape that fits your toolholder. These inserts are unhanded, so they will fit both your left-hand and your right-hand toolholder.
But you are not done. DCMT211 inserts are available in literally thousands of combinations of grades and chipbreaker styles, all of which are proprietary to the various insert makers. Again, you will have to pick specific inserts on the basis of A) what material you are cutting, and B) whether you are roughing or finishing.
Once you know this information exists in an organized form, you can learn it yourself. The industry standard designations are published all over the place, and you can always consult manufacturer's catalogs for proprietary details.