I thought starcraft 64 was just a console version.
It's also not the best port ever, and playing any RTS with a controller is rarely described as better than "wonky". Split-screen multiplayer, I can't even imagine.
As for actual advice, regarding what can attack other things, the main issue there is ground vs air; any air units that can attack ground and run up against some ground units that only hit other ground units, will of course dominate. Been a while since I played, but I'll give some brief race info on what I remember that will hopefully be useful.
Terrans: The "versatile" race. Their weakest units, marines, are the only ones that can attack ground and air out of the 3 races, and many of their buildings can lift off and fly elsewhere, good for making a new base or escaping enemies without anti-air. Terrans have the strongest defense. SCV's can build bunkers, which house infantry units (marines, firebats, ghosts, have to be manually sent inside or out) and protect them while they fire on the enemy from inside. Possibly the unit most worth noting is the siege tank, built from factories. In siege mode (has to be researched and set manually, prevents movement) they have enormous range and damage. Place them behind bunkers to keep them safe from anything that gets close. A substantial amount of siege tanks can annihilate almost any ground force, at greater range than they can fight back from. Terran buildings/vehicles can be repaired by SCV's, and buildings will catch fire when badly damaged, and must be repaired quickly or they'll burn down.
Zerg: Have weaker units but can make them more quickly. All Zerg units are hatched from larvae, which come from hatchery buildings. This can be taken advantage of, in that they can have 3 larvae at once, whereas any other building only trains 1 unit at a time. Zerglings are your cheapest, earliest unit, and can do some serious damage in swarms, but tend to become irrelevant in mid-game. They can be dangerous again later, with an attack-speed upgrade and the capacity to spawn huge numbers with multiple hatcheries. Hydralisks are your next unit, and you'll probably want plenty, since they can attack land and air and are decently strong/cheap in large numbers. All zerg buildings except for hatcheries have to be built on creep, the purple goo that comes from hatcheries and creep colonies. If the source building is destroyed it slowly recedes, but you can rebuilt another colony before it pulls back. Zerg buildings/units heal over time, but can't be made to do so faster. Zerg defensive buildings aren't especially strong, and are best used to hold up enemies with support form units.
Protoss: Strong but expensive units. Zealots are your starting unit, and twice as expensive as marines (4 times as zerglings), but are much stronger. If you have 8 zealots and see the enemy has 8 marines, that's not an equal force, you have a huge advantage. Dragoons come next, and have no particular strengths, but can hit both land and air. Their defensive structure, the photon cannon, is not especially tough but noteworthy as hitting land, air, AND being a detector. You can line your flanks with them to keep out air and infiltration and have backup defenses against any ground troops that get in. Damage to the health of protoss units and buildings cannot be restored, but all protoss units have shields that take damage before health does, and regenerates faster than zerg healing. Archons are very powerful units that run almost entirely on shields, made by combining two high templar, and are notable for their abnormally high gas-to-mineral cost. If you can control multiple geysers, the fact that they keep producing small amounts after being depleted makes archons the most economical late-game units. Protoss buildings have to be built in range of a pylon's energy field, and these pylons double as your population limit, so you'll want plenty. Those buildings will shut down if deprived of energy, so don't put any pylons powering your defenses in a vulnerable spot.
General:
-All races have a long-range siege unit: siege tanks for terran, guardians (upgraded mutalisk) for zerg, and reavers for protoss. Use them to hit enemy defenses from a safe range, as well as to protect your own base from shorter-range units and other siege units.
-All races have cloaked/unseeable units, and detectors that let you spot them. Make sure to have detectors on hand, especially at defenses and with attacking armies, so that invisible units don't tear them apart.
-Try to learn and remember which units can or can't attack ground and air. Hitting a group that can't fight back is a big loss for the enemy, and victory for you.
-Military units aren't the only ones to think about. If an enemy leaves their base undefended on the sides or back, flying units, transports, cloaked infiltrators, and so on can sneak inside and hit their resource gatherers. Wiping out the enemy's income can badly slow them down, and if you wipe out all of them and the building that makes them, you can doom them entirely.