Just some additions:
-at start, build 2-5 scouts, depending on the map-size. Set them on autoscout, but keep an eye on them and disable scouting and make them stop as soon as they pass neutral extractors. Your scouts can occupy those, which is extremely useful and boosts your economy A LOT!
-build an imperial lab and a military lab at start. Research assailants (military) and the terran population upgrade (civ tree)
-use the rest of your supply for assailants (should be 8-12, depending on how many scouts you've built). Upgrade your fleetsize then (you should've colonized the asteroid close to your planet in the meantime), and keep building assailants until you got at least 15. Set rally point of your planet on your cap, so you don't have to keep sending them after it.
-when you got that roid, choose (depends a lot on the map as well):get a mil. lab there and get some sentinels(about half as much as your assailants should do fine) for fighter-cover (your current fleet is pretty much screwed if your opponent has carriers) or build an imperial lab for ice/volcanic planets. Basically, if you're rushing don't bother with too much civic upgrades.
-while your fleet is on the move, or if you can afford it (did you grab those neutrals?) even earlier, upgrade phase missiles and your hull upgrade (it's cheap, so it's a must-have!). The first 2 hull upgrades suffice for the moment, but upgrade the missiles whenever you got enough labs!
-again, your scouts are useful: keep building them in case your enemy is trying to keep posession of neutral extractors. Those things are, again, worth A LOT. 0.7metal/crystal per second translates to about 2creds/s if you sell them. That's more than a tradeport, and it's virtually free! Moreover you should keep an eye on your opponent with them, see what his fleet consists of and counter it (he got illums? get carriers fast. LRM? your assailants can handle those. carriers? I Hope you got those sentinels, then).
Oh, on a sidenote: the heavy cruisers are called enforcers (and their slow is pretty awesome, costs no antimatter so the enemy fleet is perma-slowed!). Marauders are one of your capital ship classes, though a fleet of them would surely help
Edit: Aw, man...Amish...stick to questions about your scout-rush, this is finally something I can help with as well
Edit2: The marauder is a viable counter to the Marza's Missile Barrage, so since your friend plays them: you might want to get that as your 2nd cap to phase out the Marza as soon as it starts the Barrage, he'll be infuriated. TEC-people really don't like wasting a MB