A class stars contains a good amount of earth likes. B class can harbour the odd one.
But yeah, the system's heat creates the available zones for planet types and their mass (usually) dictates how big and how many planets you can get.
The optimal star size, if you're looking for a good sized goldilocks zone with a high probability of terraforming-sized planets is the F class. Planets in A class systems are often over 4 earth masses, pushing them above the terraformable size set in-game.
The stellar forge also seem to have set patterns for each star type. From the tens of thousands of jumps I've made I get the impression that G class stars has an abnormal high rate of systems without planets in the goldilocks zone, but plenty of Mercury-type planets combined with gas giants. O class rarely gets planets, but if they do they tend to be massive.
Beware that stars with one or more binary stars gets their zones extended outwards, if those stars are close enough.