Hi soulieberlin!
Stellar sovereign economy requires a bit more unconventional approach then other games, first of you should not worry about not having excess money all the time. In the beginning your two best bet is high taxes and selling your resources on the market.
Selling resources is almost equivalent to cheating in my experience. Send your mining fleet to a new system, when it mined around 50% of its current location, the reason is that they mine out the rare resources in the beginning and after that they mostly mine common resources that does not sells well on the market. Later you may want to colonize a planet with high resource yield and sell it on the market each turn.
Regarding population growth, migrate your pioneer population to your second colony that frees up space at your capital. It also helps to pick a government type that lowers the cost of housing development.
About importing food; indeed, you need a trade connection to the colony in order to import goods, but you do not need a trade station at the receiving colony. Use the trade station of your homeworld and establish a trade route with your second solar system, then assign freighters to the route and begin importing from the capital.
Research is indeed expensive at the beginning but there are numerous opportunities to mitigate it over the course of the game, there are technologies, traits, bonuses, events and a treaty that can help you with that. I also suggest to half the research cost at the start when you set up the game.
And you may consider picking the random technologies starting bonus, it gives you 10 random tier 1 technologies.
About research bonus, it starts out small, but can be grown until +999%. Each research station provides +5% and what the system has, as well as +1% after each lab module.
What is a bit unconventional about Stellar Sovereigns economy is that you cannot easily afford all that you have access to, so you must prioritize. I know it is frustrating that the population may protest your hight taxes or that their growth is caped, but you building a new capital vessel so they just have to suck it up. On the other hand, when your shiny new ship is built, you ease up for awhile and develop your colony.
Thanks for your feedback, please provide suggestions, ideas on how to approach balancing the economy and I will do my best to implement.
p.s.: You may enjoy Altron’s series: https://www.youtube.com/watch?v=O6hEQ0liDm4