Ubers: These are the core of what you will field in campaign. Sturdy, great stats. Though not the whole show given that some missions limit what type of units you can bring, you will need some teams of other soldier types. The expense is relative, given how hard it is outright lose an uber, and the numerous methods to get some extra recruits you don't usually buy alot. I've played campaigns with "found" ubers only and didn't even feel any pressure from it.
Peasants: Not great but they are cheap and given time to train are very nearly equal to slave soldiers. These are likely to be the bulk of your garrison troops in the early stages of base expansion. And the handful of "non mutant" limited missions does mean you need some of these ladies.
Slave Soldiers: Garrison troops once you have the ability to get them in similar numbers to peasants. Thou i do include a handful with the gals in later game cause the testudo armor is the tankist, non codex locked armor. Also no morale degen is handy on certain types of longer missions. Same as with peasants you need some non mutants to handle the full spread of missions.
Lok'Nars: Not usually included with the major combat teams. But cave environments mean you do need some. I do use them quite alot as pilots thou. Aside from a lucky freak they have the best starting reactions so they are usually good pilots right out of the box. Second best pilot when dealing with stat capped troops but usually you want those capped out gals doing something else then air combat.
Bugeyes: I include one or 2 with the major combat teams to fill the role of nurse, since they are far superior with there default outfit then the actual nurse outfit being used by any other type. Good voodoo stats and inbuilt psi amp mean they can still help out even with there hands full. Also very good in fixed darkness missions, like underwater or space due to extra vision range. In alot of cases they outspot the natives of those environments. Sadly not alot of outfit options limits them even in there best environments. On paper the best voodoo user, but other classes have better voodoo booster outfits so that advantage is marginalized to top few percent of rolls for voodoo str.
Auxilia: Supplement the garrisons as beast housing facilities are cheap. Mutant reapers and werewolves(if your lucky to get some) are really powerful defenders. Even the basic doggos are pretty useful, once strapped with pre primed explosives. There is a case to be made for using the high HP types in place of HWP armors since they fully regen between battles so chip damage won't put them out of action. Usually becomes irrelevant once you have the heavy tanks, since those can face tank pretty much all direct fire without harm to the pilot.
Gnomes: They have a very unique stat spread which makes them the ideal offensive HWP operator. There reactions aren't quite up to snuff so defensive posturing HWPs with them is not very good. But given that they can use all HWPs aside from the quad and the assault bike and have higher HP caps then anything but gals, while being immune to Psi attacks(min 120 starting bravery) makes them really powerful. Also a bit of niche in Voodoo str scaled tools like wands, highest Vodoo str and the bravery to mostly not care about morale costs. Lousy psi skill thou so the full range of Voodoo is beyond them. At the moment stupidly rare due to being only "found" recruits, and from a damn limited amount of missions. At present the single rarest class. If you make the right choices you will see 1 assured chance at one.
Syns: The one type OP missed and previous holder of the rarest soldier type. Properly equipped syns, make even the gals look frail and pitiful. Native regen, ridiculous damage resistance even in there "naked" outfit, immune to psi and morale, and can rip open tanks and power armor with there default melee on a number of outfits. Also can be resurrected if you somehow get one killed. Two big downsides, no voodoo tools(or stuff scaling off bravery), and energy management issues lead to severely limited sprinting. High TU so you can get pretty far even walking and are very deadly with fixed cost weapons. You get 1 during play normally(in similar manner to you first freak) and might find more if your lucky with space missions.
My main team is mostly gals with 1 Bugeye as nurse/psi support and any syns that turn up.
A second team is Peasants/slave soldiers rolling a convoy with HWP support, same team with some modifcations also handles the non mutant encounters. Although this is usually late to the party as it takes awhile to tech to and build up the gear and facilities for this to be anything beyond a exercise in attrition warfare.
Third team is a mixed group of gals and bugeyes for underwater/space once i have space suits for everyone. Something of a luxury thing in late game so i dont have to go microing craft/gear loadouts, but its a whole base worth of hangers and the attendant support facilities, so its never very early. Late game you can set this up in a single hanger as apposed to 2 with the dragon craft.