even playing against the computer, you have to make decisions in real time about research, so i need to know the tech tree by heart.
You can pause the game while viewing the tech tree (or anything else for that matter). Just press the "pause" button on your keyboard while you familiarize yourself with the tech tree.
Sometimes I feel like I'm haphazardly researching stuff...
Common for beginners. We all did it when we were starting out. You'll eventually get a sense for which situations each technology is useful in. Experienced players generally get very few technologies (mostly unit prototypes), instead focusing on the ones that will best help them in their current situation.
I feel like I need to get 2 civic labs up right off the bat so I can get trade ports
Don't rush into trade. They're great late game, but early game they're a complete waste of time and money. Colonizing new planets is a way better economic investment. People underestimate what a few extractors on a newly conquered planet are worth; they forget that every time they go to the black market to buy crystal or metal they're usually paying 450-500 credits for 100 of the resource. A new planet with three extractors is worth more than building two new trade ports, but costs much less.
Long-term: it's the planets you control, not the infrastructure you build on them, that count. If I control 8 planets and you control 5, it doesn't matter if you have trade ports. It's going to be a hard fight for every planet you want to capture, whereas I can easily build trade at any time I like. Your priority is to secure an empire early game, and you're digging your own grave if you compromise your early-game expansion.
but when I do that it means some of my basic mil upgrades come later... like hull plating, lasers, etc.
More importantly, get advanced unit types and repair bays. I can't stress the importance of repair bays enough. Other important units to get are the Hoshiko support cruiser and Javelis LRM. The basic armour and health upgrades are pretty good, but the others are a tad expensive and you're better off building more units than getting extra damage.
Any thoughts would be great on what the generic starting path would be...
Scout before you build your labs to find out how far away the enemy is and what planets are nearby. The reason for civic labs early game is to access ice/volcanics, so these are what you're paying attention to. If the enemy is far away or there are many ice/volcanics between the two of you, go for two civics. Otherwise, go for military. You can always pick up the other technologies at a later point in time, but almost always you want two of each type of lab.
Also, any thoughts on the types of gameplay that the AI does depending on the "type"? Like Economist, Fortifyer, Agressive, Researcher?
They all play roughly the same, they just have slightly different preferences in terms of units and structures. They all tend to over-spend on defense and under-spend on military and military technology.