The HC also have the added bonus of them being true CMOS devices and many ( though not all and YMMV depending on manufacturer) will work from 3V to 15V as a power rail.
74
C is roughly equivalent to CD4000 series "metal gate", high voltage CMOS. I think... the outputs are weaker (~500 ohms Rds(on) vs. ~250 ohms for CD4000, at 10V or thereabouts)? Both 74C and CD4000 are useful from 5-15V (though a bit weak down at 5V), and still operable down at 3V (if rather weak and slow).
74HC is the "newer" (since the '80s I think) "silicon gate", medium voltage, "high" speed CMOS. The maximum voltage is 7V, and should never be used much above 5V. The drive capacity is good (Rds(on) 50-100 ohms I think, at 5V). HC is useful from 2-6V, and still operable above, I think, 1.2 or 1.5V.
For breadboarding, I would also recommend HC. LS is good too, but only if you can find everything you need.
Do be mindful of static when working with CMOS. 74HC is more robust than very early CMOS was notorious for, or even CD4000/74C series, but it's not invulnerable. (Neither is 74LS, but it is harder to screw up.)
CD4000 series is still very handy, especially interfacing with analog circuits, when you need just a little glue logic, or analog switches (e.g., CD4066) and stuff like that. For pure logic, it's kind of janky, with relatively slow speeds, and nonsensical pinouts; HC is better for that. (If you run across a CD4000 function that you wish you had in HC, check the 74HC4000 series of course!)
Stay away from S and ALS unless you really need the speed, they are power hogs and in most cases will not work in a breadboard layout easily.
Agreed. Also, AC, LVC, etc. All those fast ones will just go nuts on a breadboard, even oscillate at frequencies invisible to the average oscilloscope!
Tim