The money penalty in a colony rush

Set tax low enough to keep morale on your homeworld at 100%. If your population starts to run low, don't completely fill the colony ships, just send them out with a token number of colonists in order to claim the worlds.

using a +pop growth bonus at race setup can also help

I only put 100m colonists in, instead of the default 500.

You could also play on a smaller map, or adjust the settings so there are fewer habitable planets. That limits the number of colony ships you'll need so you can pump them out at the beginning without taking such a major hit in the pop dept.

It is all about map size.

On the tiny and small maps I usually play, all colony ships are built on my homeworld and sent out with max population until it gets down to the low PQ planets. I let all new colonies grow without sending out colony ships unless I am just forced to rush a colony ship to grab a high PQ planet.

On larger maps, the original colony rush is done the same way but later, the border planets build colony ships to extend the empire.

I always have some economy bonuses by selection or politics and frankly, money is never a problem for me by the second year. Just research planetary improvement and Xeno econ and it pretty much takes care of itself with population growth. Econ buildings can help but they are not essential until you get to the point of wanting 4-5K per turn surpluses.

I always use my initial planets to build colony ships to grab other planets. Of course in the process, my planet's population never grows that much and thus my tax revenue in low. I never go in the red but til the middle game I am cash short unless I find some big buck anomalies. By the end I have enough colonies to overwhelm the AIs.

Your strategy is fine if it works. I used to play like that too.

Myself, I build a factory or two and then create economy buildings galore. The planet then becomes a cash cow.

only put 100m colonists in, instead of the default 500.

I always have taken 500 from mother earth to give the colony a better jump
start. Mother earth tends to stay around 5 bil as I pump out colony ships.
If you start a planet with a smaller pop, doesn't it take longer to produce things?

Or am I wrong about that?

You are right about that and that's pretty much how I play it but it is not a deal breaker either way.

Depending on Morale a .1 planet can catch up to a .5 in 25-30 turns and none of them are producing much income at less than 2.0 anyway.

I am sure there are players that can tell you exactly what the catch up rate would be. With me it is just a feel for it.

Bear in mind that if you need more colonists later (whether you send a full load initially or try to conserve your existing population base) you can move them by sending a colony ship. Then when you find a suitable planet that isn't already taken, you might be able to colonise it faster than it would take to send one from your capital.

I found the money thing to be the most difficult aspect of the game to solve.

Full colony ships with 500 m per ship is the way to go, in order to increase the tax base empire wide. The home world is not going to be a big money producing planet, so it makes more sense to ship them out. The caveat is to keep taxes ultra low to get the 100% approval pop bonus for the first 20 turns of the game. Each planet needs at least one billion pop to get full growth. Starting at 100 m stunts their growth, so I see that as a stop gap only to be used in extreme situations.

Morale techs, buildings, and wonders, money techs and buildings, higher empire pop especially on "money" planets (three factories, the rest filled mostly with entertainment, economic buildings, and farms), and better government (Republic on up) are the ways to get more cash. A player can also trade with freighters, or sell techs. Racial bonuses, and political (Fed party) help. It is also a lot easier on lower levels where the player gets a money bonus.