Well you were saying that you played on unlocked FFA correct?
Look at it this way. In real life, 7 factions would gang up on a faction, then start fighting each other later for the land. So it is in fact much more accurate for several computers to gang up on you, making it very difficult for a smaller empire to succeed. It is possible to still pull through, but in my experience with the game it is usually better to lay low and build up an economic base before starting to move out.
Remember, over-extending is the worst thing that you can possibly do. If you over-extend, even if it is only three planets, you will face a cold cold death.
Before you move on to a new planet there are some things that you should do:
1: Make sure that your fleet is big enough that when you attack the next planet, if an enemy were to jump in immediately afterwards, you can hold them off. I have, on several occaisions, captured a planet, then promptly got decimated when a Hard agressive jumped in with a medium-sized fleet and proceeded to lay waste to everything.
2: Have I completed the bulk of expansion for the planet I just conquered? The last thing you want is to take a new planet,then be dividing your resources in between the new planet and the one conquered before that. Remember that front line planets need to have emergency shelters maxed, which takes a significant amount of time and money (for time, reference point number 1). Usually a good progression for building up a planet quickly is first build a frigate factory (will explain in a bit), then build extractors, then start pumping money into emergency shelters, then build civilian upgrades. After that it is not so important.
3: How long will it take my fleet to respond to an emergency? If by some random happening an enemy fleet slips by all of your defenses and settles on a planet that would be considered a "Core" planet, how quickly can your fleet get there? This is the biggest question when you are expanding your empire. It is usually a good idea to have two main fleets on a smaller map. Your larger attack fleet moves further away from the planet exploring and harrassing your enemy. The smaller fleet stays closer to your home system and is on-call for emergencys. That is also why I strongly advise that you have a frigate factory at EVERY planet, preferable on the side that is furthest from the direction an enemy is likely to attack from. If a fleet jumps in and start causing havoc, you will be able to use the extra resources from only developing one planet at a time to build a few frigates to distract the enemy while your defense fleet returns. Combine that with a few hangars and you are golden.
On top of all of that, I noticed that you did at least recognize that the hangars are the best defensive structure. If you only spend your tactical spots on hangars, you can easily fit three into most planet types (asteroids not so much). With the typical racial upgrade for fighter limits, you are talking a good 3 wings per hangar, so with three hangars that would be 9 wings of strike craft. a 6/3 ratio of fighters to bombers is usually what I use, then adjust for later planets once I see if what combination of ships my opponent likes to use. Plop a repair platform into the middle of your hangars to keep them alove and you are done.
That is is method I use to decide if I want to move on. It is by no means perfect, and I do not claim it to be. In fact almost everyone else will probably disagree with me on several of those points, but whatever.