I only run into problems when I'm simultaneously building a lot of ships, expanding most/all of my shipyards, using all of my research capacity, all of my construction capacity and all/most of my ordinance and fighter production capacity. Just pause or cancel some of your projects until your economy recovers. As long as you have steady expansion without going overboard you really shouldn't have too many problems. Also, past the very early stages, it is generally much more profitable to found new colonies and expand existing populations than it is to crank out tons of financial centers. Build a few right off for the initial boost, but after that point tax income from populations will far outstrip everything else. FCes and taxes on civilian shipping and mining are just little bits of icing on the triple-decker brownie cake that is population.
I disagree. Building financial centers is a much quicker way to increase income than founding new colonies. New colonies are definitely good to do, but it's not going to be a quick return. They're more of a long term investment.
I'm using round numbers to make it simple, but say your growth rate on earth is 3% and you move 100 million people to new colonies and get growth rates of 10%. That's effectively getting you an extra 7 million people per year. So the colonies are like building 7 financial centers per year after you've got them there just from the extra growth rate, plus the other benefits like additional labor force and such.
Unless your construction rate is abysmal (or you find perfectly habitable worlds), it will take more effort to get those colonies going than it is to just build 100 financial centers on an existing world. You have to either terraform them, or move infrastructure in. The infrastructure your civilians can do, but if you were trying to focus on doing it faster for wealth increase you'd have to manufacture it and move it in yourself. Terraformers can obviously be reused, so investing in them is a great long term investment (I like the ship ones myself) - but if your economy is in the red you need financial centers first.
Plus you can easily do both at once. The best way to build economy is a combination of the two. Seed your colonies and let your civilians handle the infrastructure. Haul in construction factories and minerals to a colony and have them build financial centers. Also consider the bonus for financial administrators. Plop a 30%+ wealth bonus admin on a developed world full of financial centers and you have a real economic powerhouse that can feed a massive research and construction budget. Unless you have a whole bunch of + wealth creation guys, it's not as easy to do that with a bunch of colonies.
A benefit to building them off earth is you can use earth for something else, like as a major construction and shipbuilding world with all the workers doing construction and exporting things to other worlds.
I had a game where I moved my research to Mercury, built Mars up as a massive financial powerhouse with 4000 financial centers and a 50% wealth bonus admin, and had Earth with a 40% factory production rate boost admin and was churning out installations and ship parts and ordnance and everything with incredible speed. Mars produced around 400k a year. I managed to spend it all though, had construction factories all over the place constantly building stuff and I had 200 research labs on Mercury doing various research. Eventually I got bored of that game and started a new one. That was one of the few games where I focused on turtling up in Sol for a bit before branching out, and while it's wildly effective for making a super advanced race that can kill anything, it's incredibly boring once you CAN kill anything. I even turned the invaders on, and their invasion didn't do so well when faced with an enemy that can churn out enough ordnance in a day to lay waste to their largest ships. Even their special tech doesn't do so well against an alpha strike of a thousand warhead 64 missiles.
edit,
I've build 500 financial centers and I'm at -60 undefined wealth units per undefined time unit now.
I think that'll do..
Hehe, the -60 is for each construction cycle - just short of 5 days. Unless you hit a 30 day turn, in which case I think it shows the total for the month. You must be spending a lot to have 500 new financial centers and still be in the red.