I’ll give this a shot.
Sure, you could. It might be a little weird, and man are you gonna have to have a lot of units, but yeah.
I would avoid monsters that highly encourage particular unit selections. For example, Sky Sentinel really likes having Strike Fighters, and (the way I play him) a decent portion of his kit is about having hard-shooting Strike Fighters and Rocket Choppers.
Assuming you’re playing Protectors, I’d avoid the following:
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Sky Sentinel and Legionnaire, because both of them want a lot of Faction units to make their kit function.
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Vegetyrants monsters, because they really like having an almost entirely Faction-pure unit selection.
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Zor-Raiden, because, in my opinion, he’s a somewhat weak monster. (I don’t like saying that, but he’s really one of the two or three models in the game that I’d hesitate to recommend. He’s a guy who’s sort of good at punching in a game about making big, splashy power attacks.) (I’ve tried him; I really have. But I can’t figure this guy out.)
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Zybanos, because Dragon Storm is a complicated rule, and he wants a lot of Faction units to make full use of his kit.
I can make similar suggestions for Destroyers, but it seems like I remember you talking about wanting Protectors at some point. 
You’ll need 30 units for a 1-monster game, and 40 for a 2-monster game. You also need dice and debris tiles and whatnot; you really couldn’t go wrong by picking up two starter boxes for this purpose.
Beyond that, I’d recommend the following unit boxes as generally solid all-rounders.
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G-Tanks & Repair Truck (good back-line securing units, plus Repair, which is half the reason to play Protectors)
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Steel Shell Crabs & Psi Eel (good defensive units, plus a solid specialist)
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Strike Fighters & Rocket Chopper (all-around useful)
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Carnidons & Spikodon (the best melee units in Protectors, plus a solid shooter)
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Fusiliers & Warder (so long as one player can draft multiple Fusiliers)
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Gargoyle Monoliths & Temple Monolith (almost ideal in a draft format, so players can get some variety)
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Ocean Hydra & Man-o-War (so long as one player can draft all the Ocean Hydras, because they’re the best shooting units in Protectors, and the Man-o-War are good defensive securing units)
That is only 35 units, but I’d hesitate to recommend anything else. Maybe toss a couple more random unit packs in there just for some variety and personal choice.
The Elemental Champions unit boxes are all solid picks.
As for buildings…hoo boy. You’ll need a minimum of 12 buildings, 6 per player. Realistically, you need 10 per player, because otherwise any map besides Isle of Annihilation is going to feel super empty. I’d say the best thing to do would be to buy two each of the new “Building Set 1” and “Building Set 2” packs, and then maybe grab a few extra buildings that catch your eye. If you get a starter box (or two), you’ll get good use out of the cardboard apartment buildings, which will dramatically reduce the cost of this endeavor. 
Beyond the cardboard apartment buildings I’d recommend the GUARD Defense Base, Martian Command Post, Jungle Fortress, and Mount Terra as the most generically always-useful buildings beyond the stuff in the two printed building packs.
Lastly: if you just want to get your friends into the game, you can play perfectly serviceable 1-monster games with 1 monster and 10 units each. You won’t quite get the full experience, but it’s good enough to convince your pals to get their own stuff and chip in. 
Hope this helps!