Pantone solids are created from more than just 4 colors. They're mixed from 10 or 18 inks, depending on which system. They're a little bit secretive of this!
As an example, here is the gamut you can achieve from 3 and 7 colors. Now imagine how many more colors are possible from 18!
And after that point, you are likely reaching diminishing returns, as all of your solid combinations are well covered by a mix of your primaries, and you'll reach the limits of human vision. :)
The letter following the pantone color number indicates what Pantone system (or book) you're using. For most print & web designers, you'll likely want the Pantone Bridge books to look at colors from your design program, to real solid ink on paper, and real screened CYMK on paper. The type of paper, coated or uncoated, can also have a dramatic difference of appearance for the very same solid ink. This is important if, for example the cover of your book will be coated, but the text block is uncoated—you may want select two different colors!
- C = coated. It is solid ink on coated paper.
- CP = coated, process. It's a mix of screens of CYMK, little dots that appear mixed when viewed with the eye.
- U = uncoated solid.
- UP = uncoated process.
Your professional offset press print shop can print solid colors, but usually their press only has 6 or 7 ink capacity. C, Y, M, K, AQ (aqueous coating), UV spot (spot gloss), and one spot for you! Spot colors are more expensive as they require mixing, cleaning the ink well, dialing the color in, as well as the ink itself. Typically this is done for logos, or important product colors that you don't get a good replication of with process colors. Also important to consider are solid colors print more cleanly at very fine line widths than process which must go through screens. If you MUST have more than 6/7 inks, you'll get to either use two presses and pay the color change fees, or run pages through twice, waiting for dry times and pay $$$. Also hope your solid is in the correct order for your design, or you'll have to run it through again!
Now lets talk digital presses. Some fancy new digital presses can do spot colors! This used to be reserved for offset jobs only, and if your job run was not large enough to meet offset printing minimums, you were stuck with digital and no fun special effect inks, or solids. I have not seen these presses in the wild, but I do understand they exist from this article: https://www.mohawkconnects.com/article/mohawk-blog/understanding-spot-colors-and-their-role-digital-printing I expect you'd also have additional set up fees for spots on digital printing.
I would ask other local print designers for a good printing rep and begin a relationship with them. They will be happy to give you a tour, give you paper samples and pantone chips (you'll need to buy your own books though, sorry) and advise you when quoting out jobs on the most cost effective ways to design and print your projects. Ask to do press checks on your big jobs (extra cost, but pass it on to client) and you'll learn even more. Call them up when you start to design a job, and they can even find samples of similar printing processes that you want, so you can show your client why they should absolutely pay for a product thats offset printed, UV yellow on top of a double hit white, on black stock. :)