You can start with wall combos such as ferrothorn and jellicent which both cover each other's weaknesses. Having good coverage is easier than trying to resist everything - so a water - fire - grass core would deal at least neutral coverage to everything and having ghost + fighting moves on one pokemon also has neutral coverage to everything.
Pokemon with one weakness include Kingdra, Scizor, Excavlier, Bronzong and forretress. They also resist a lot of types. Also normal pokemon are only weak to fighting lol. Steel, water, dragon and rock have the most resistances.
Elektross, spiritomb have no weaknesses and shedinja has a lot of immunities, but also a lot of weaknesses.