My personal rules of thumb- first few years prune EVERY clem down to 2-3 nodes, if you not sure wait a little until you can kind of compare and get a feel which node is looking like having life and which does not. After clem has at least 6 stems coming out I prune hard those that bloom late and easy/ just minor cosmetical/ those that bloom early. I leave alone anything that belongs to group 1/ blooms the earliest for me/ and especially tough large stems.

Now is the time to prune if you haven't done so already. If they are all three years old or less, prune them all like a Type III, which is the most drastic type of pruning. It helps them get off to a good start with their root systems and put out more stems from the crown. Prune just above the lowest set of new buds. Petit Faucon is an Integrifolia and should be pruned to the ground every year. I don't know about Crispa but the rest are all Type II's.

Looks like Jackmanii to me. I would prune it like a type 3. I prune back to 2 leaf nodes late winter each year. You may get other opinions but that bloom doesn't look like any type 2 clematis I know of.

Starchild, many plants will grow fine without our help but some will look tidier or fruit more or bloom better or have fewer diseases if cared for as recommended. So I water my tomato plants if it's too dry (though it rarely is here, but might be different if I wanted tomatoes in NM), remove old peony and phlox stems in the fall to reduce the following year's diseases, and I hard prune certain clematis so I have flowers at eye level rather than only at the top of a 10' plant and to avoid looking at a tangle of dead stems all winter. However, in the case of this particular plant, Clematis Serious Black, it is just a matter of removing last year's dead stems for tidiness. They are one clematis that grows totally new stems and foliage each season and what beautiful new growth it is!