What's the difference? And do the majority of people online have mics?
Racing Series are generally a set number of races, usually one per week. There are many different series with different sets of cars to choose from. A race series would be something you could commit to every time it races, generally speaking. While they do let you miss a race, but they usually only have so many spots and if your only going to be there one race out of 10 then that's probably not what you want to do.
Clubs & Leagues are a bit more relaxed and less stringent on you showing up to every race every weekend(day, whenever.) The race/car is usually mixed from one week to the next. Whereas the racing series you most likely will pick a car and race that for the duration of that season. Some race series let you change cars, but mostly what you pick is what you got.
Having a microphone is a bit help, it's much easier that typing out a long message only to find out the PSN chat filter has blocked your entire message because you said "engine" or something not offensive. Some race series/clubs will not use the microphones during a race to limit lag, but some just ask that you turn off your microphone during the race and only use it if it's a pressing issue during the race.
You will see some rooms in public lobbies that say something like "Microphone Required", but if you joined a series/club and you didn't have one it's not the end of the world. It's a nice investment to make. Especially if you get a microphone/headphone combo.
What I use
Most all Race Series and Clubs/Leagues abide by the GTP OLR rules. Some modify the rules a little bit. Most people that race there expect clean racers.
GTP OLR
And in general you'll find more mature drivers in the Race Series/Clubs & Leagues than you will find trolling through the online lobby scene. Sure you'll find a good room every now and then.
Hope that helps.