What tech tree are you using? That may be the problem because some tech trees simply fall behind early in the game like Thalan tech tree. With Thalans is where I often have that sort of problem because they have no industry or research normal buildings for awhile and the first ones are very nice bonus's but very high cost and newer vesions just lower cost. Imo Thalan and a couple tech trees require you to trade/steal/buy other techs as a stand in. Thalans are just very slow starters other then a few super buildings off the bat.

If thats not your issue how are you building? First turn generally I buy a research building and factory on turn 2. Keep worlds under 12k pop besides capital (never use farm tiles for farms and no more then 1 farm). Generally do 2 factories, 2 research, 1 moral, 1-2 econ buildings, 1 farm (maybe), and inf building only if tile (maybe). and of course starport.... generally 1 of each building until thats about done and pop is getting up then add in second. Couple high quality worlds get filled with either labs, factories, or econ buildings for those capitals. Asteroid mines are pure love as free industry after built, and keep them upgraded. Rush buy a colony ship or a completely empty freighter first turn and upgrade it second turn to a colony (add to homeworld to fill fully and its cheaper this way by 300 credits or so). Get a couple scouts then back to colony ships. When a handful of colonies get a couple miners followed by survey ships.

Also never forget those econ starbases are great when upgraded. Cheap extra industry and trade freighter bonus's. Fit in whenever you can constructors to grab nearby resources and get them mining as you need. If find a few hostile races nearby get a few defenders after your initial colony rush just for some mil rating.

Youve probably already seen it in other threads, but the one of best bits of advice ive seen so far is to not build on newly colonized planets instead wait for them to start making a slight profit then start building.

I'm playing on huge galaxy as the Altarians, as the federalists, every opponent slot filled. I try to avoid bankruptcy because you can't buy anything while your in debt (unlike the U.S.), and your approval falls every turn/ I put bonuses on Social/Military, research, pop. growth.

Some things that you may not be doing at the moment:

1. Get production up at your homeworld (typically rush-buying 2 factories, then building another one), then crank out colony ships
2. Colonize all decent quality planets you find (I'd say around quality 10 or better would be fine). Get factories and a starport up at 2 other planets. Beyond those 3 initial planets, don't build.
3. Research cheap technologies that give you a decent boost to social / military production or economy. However do NOT forget to research better engines and modify the design of your colony ships to improve their speed. This is crucial in colonizing planets before the AI gets them.
4. Do NOT forget to research sensors. Design a scout ship with survey module. Create a handful of those, let them auto-survey. This should increase the number of times you get 250 or 1000 bc in cash from surveying an anomaly.
5. Keep taxes low initially, stay at 100% approval rate until you drop below 1500 bc. Then go to 76% approval rate.
6. Research in order to get manufacturing capital, tech capital and econ capital early in the game. Dedicate 1 planet to production, 1 to research. Build your econ capital on your homeworld.
7. Once you're through with the initial cheap techs, research new government types. This will give you the federalist bonus, better diplomacy in negotiations and access to the political capital which you should build on your homeworld to get approval rates up.
8. As soon as the population on your "other" planets (meaning the ones you left empty) has reached a certain level, fill those planets with economy buildings.
   There are 2 possibilities:
   - if you still have some buffer before running out of cash (about 30 turns or more at the current spending level), build as soon as the planet's income is so high that the econ bonus from your econ building is higher than its maintenance cost. E.g. if you get an 8% bonus for a econ building and its maintenance is 1bc, you need an income of at least 13bc before building econ buildings.
   - if you have little cash left, wait until the planet's income is more than its spend + maintenance cost
9. Trade: sell 999 influence points at a time for cash or for useful technologies. I typically try to get any technology that I don't have access to because of my race's tech tree, especially the ones that give me a % bonus on tech, morale, economy, social/military production. Keep it cheap though, if you have to pay up to 200bc on top of 999 influence points, that's fine but then sell a few times 999 influence points so you're making a profit on the transaction in addition to buying technology.
   With some races you can get 1-2 scouts cheaply for a few hundred influence points. This saves you the time of building them. Simply add on a survey module and let them auto-survey.
   You can also sell some basic technologies, especially to minor races (e.g. stellar cartography which doesn't help them) but never powerful weapon technology or diplomacy techs.
10. Once you don't need as many colony ships anymore, produce a few freighters at your homeworld, then send them to other races' capitals, preferably distant ones. This helps both for income and for keeping good relationships with the AI.
11. After 1 year, get research (and if possible, economical) treaties with the AIs, as long as the price is reasonable compared to how much cash you have.

At all times, keep an eye on the military ranking. As soon as you see 1 race going above zero, research some basic weapons + preferably go up to medium hulls. If you have access to the "total majesty" tech, now is the time to get it as soon as possible. Then build a spin control center and have a few medium hulls in that planet's orbit.
Like Ralphnader indicated, from this point on regularly research some military tech. Keep your strongest ships in orbit of the SCC planet to stay ahead in military rating.

Something else that seems to work all right for me (Though I haven't played the most difficult levels, but have won some challenge games), is to try and be the first person ot research the extreme colonization technologies.  You won't be able ot fully use these planets for awhile, but they will provide money once they grow a bit, and will provide access to planets (for a time), that other races don't have access to.  (Though this does rely on having a good research advantage.)

In military terms, I've usually waited for some time to get my infrastructure set up effectively before going for a bunch of military technologies, though this could very well not work as well on higher difficulties.  On normal, though, it's worked fine for me, since even with diplomatic penalties, races will often not be able to, or not dislike you enough, to invade planets or attack very much at all.  If you do something like this, make sure that when you do research military technologies, make sure ot research far into the tech tree (medium/large ships, level 2-3 weapons and armor), and choose the research to counter other race's weapons.  (You can check in the diplomacy screen what weapons and armor they are going for, generally, a pattern emerges where many of the AI races will go for similar technologies.)