I'd like some advice on how to run a economic and military game and the same time and try to balance it out as much as possible.
Typically you should be a little further ahead on the military tree than the economic tree. The reason is quite simple really: a good economy means nothing if you can't defend it. As I've mentioned before, acquiring new planets is a better way to build a strong economy than building trade ports or any other structures. As a result, one of the best reasons to get some civic labs early on is to access ice or volcanic worlds. Capturing one of these (especially if it has 4 rocks) will pay off way faster than any trade ports.
Usually I reach the 3-lab level for military before I even start civic technology. This gives you access to all the staple units: carriers, flaks, LRF's, and the best support cruisers (Hoshiko and Guardian). There are reasons to start the civic path earlier, but always make sure you have the ability to defend yourself and good reason to be bringing out civic labs quickly. Typically you shouldn't go for the civic path early on unless you have allies covering your flanks or the distance between you and your nearest enemy is 6 or more jumps.
The civic tree is a little trickier than the military tree. It's similar in that you have to think about what techs you want, and to put up exactly as many labs as you need. It's different in that it's often very hard to forsee your position five minutes in the future. Just because I want trade ports now doesn't mean I'll be in a position to build them in five minutes after my labs and the research are done. Maybe I'll be attacked in the meantime and I won't be able to put up the money for the structures.
Never go overboard on the civic tree; get as many labs as you need and only the techs you need. Don't rush into trade ports. They are to your economy as a second capital ship is to your military. A great asset, to be sure, but a huge investment to bring out and extremely risky. Make sure you can support it first. Advent typically can stop at 3-labs. They have a couple decent techs, but after the 3-lab level there's nothing really fantastic until allure of the unity, which isn't worth plotting down 5 labs. TEC usually can stop at 4 labs, although it does have useful techs along the way up. Vasari can also stop at 4 labs. Their high level techs are more strategic in nature (like phase stabilizers). Whether you even want those techs may vary based on your strategy and situation.
On the military side, there isn't much for TEC or Vasari above the 6-lab level, and usually the 7 and 8 lab levels can be ignored entirely until the very late game. The only poor level for Advent is the 4-lab level. Not much there. The 5-lab levels gets your repulsion and plenty of other useful upgrades, the 6-lab level finally gets you your armour upgrade. The 7-lab level has lots of goodies (but lots of prerequisites, so no need to rush to it), and the 8-lab level gets you mass transcendance. Probably the best balanced military tree at the higher lab-levels, compensating for that shabby civic tree.
advice on defenses, and what upgrades to get and when
The repair bay is the number one defensive asset. It makes everything else that much better, and can be used to repair an offensive fleet after it retreats, giving it higher versatility. A lot of people like putting frigate factories in there so they can build a fleet during the battle. With repair bays, your numerical advantage will grow and the enemy will have to retreat. I personally don't like this since if you do it on several planets the logistics cost adds up, but on a front-line world it's great.
As for luring people into traps, it's always good fun, but be mindful of falling into one of their's. The winner of any contest of traps is always going to be the one who scouted best, because he'll know the tricks the enemy has set and know how to deal with them. For this reason, you should pay attention to how your enemy scouts. If you can figure out whether he auto-scouts or manually scouts, that tells you a lot about him. A manual scouter is very likely looking at everything his scout does, so you can be sure he's an attentive and meticulous player. Unlikely to fall into a trap he knows about. An auto-scouter may not even be paying attention. However, you need to look at the fine details to determine whether the scout is being ordered manually or automatically.