Well most of us play on random maps in general online so if you ever want to get into the field you should play these the most.
What exactly have you been doing to lose so quickly to the Easy AI. It be nice if you can post a replay or something.
You probably want to start with a 4 player medium random map
I am mostly an avid TEC player both online and SP and generally this is probably the easiest of races to get into for newbies.
1. As your first capital ship you should start off with a Sova (assuming you arn't rushing use missle batteries and fighters) or a Akkan (with colonize ability). These are essential for rapid expansion of your empire. The Sova (preferabble to get 2) will destroy any and all militia quickly. The Akkan can just colonize and run while you place turrets to kill off the militia. If you use the Akkan then make sure you kill of siege frigates first. LRMs you can deal with by adding a second turret once they fire on your first.
2. In random maps most of the time you have a astroid sitting next to your homeworld. Get this immediately and you can do this quickly and easily with a single colony frigate. Rush your colony frigate to colonize the astroid. The siege frigate will start to bombard but if you put a turret right in front the frigate right at the closest point to the astroid. It will back off for a second and the turret will proceed to kill the frigates and you can jump yours out. This saves some time rather than spending and sending more ships to kill the militia.
3. You should expand your empire to vital chokepoints around the map. Once you have these just completely lock them down with a Starbase. With your starbase you should have at least 2 repair bays(preferablly more), 2 frigate factories, and a small fleet to deal with ships such as Orgovs and LRMs. Upgrade your SB to full because AIs always have the tendency to suicide rush them.
4. Once that happens you should work on your economy to a sufficient level. Trade ports at all your planets will do them well. If you have a desert that isn't on the front lines fill all of the logistic slots with trade ports. Planet upgrades should be limited to population (so you don't lose money on them - get these as soon as you get the planet) and logistic upgrades.
As for units the LRM is going to be your main frigate for the most part. Hoshikos (repair cruisers) are essential for any TEC fleet as they are probably the best support cruiser in the entire game especially with demo drones. Have a couple flaks here and there to deal with fighters. After that the units you choose are just mostly preference when it comes to AI.
Also the AI will send units against you so it's best you fleet a little bit early with 2 military research stations off the bat and get a few LRMs as quickly as possible.