Forget the modified scouts. Only get one of those and it should take no more than 2 turns. Build transports and head them off to different stars around you. Use the minimap and try to expand near any neighbors you have to try and grab any planets they have.

MODIFY YOUR COLONY SHIPS WITH ENGINES! I cannot stress that one enough.

First: DONT BUILD FARMS

Population above 5 billion quickly murders your approval rating, which murders your production, which murders your tax revenue. When starting out with the game, never build farms. You can more than sustain massive war going star empires without a single farm. Can farms help? Yes, but untll you get the flow of the game down, leave them alone.

Next: Always start with "Stellar Cartography" if you are using a custom race. You need to know where the planets are as soon as the game starts so never start without it. As has been suggested, you should be sending colony ships out like mad that first few turns. Custom build a colony ship with a single colony pad, a couple life support and at least 2 or 3 engines, as many as you can fit on board. After you instruct the colony to build it, buy it for full price, and do this everytime you find a new world to colonize.

Send the colony ships out to nearby stars, and do the same with your flagship. Personally, I dont bother with the level 4 world in my home system until later, it isn't worth a colony ship at the start. Any world you find of quality 9 or more should be colonized as soon as you can get a ship to it.

Some of this might be obvious but the starting land grab is the most important 20 turns of the game usually.

A few pointers for the midgame:
Do not over build. Yes you need good production, but not every world should be maxed out as builders. Social spending is a little broken right now, and any unused social production is lost (you still pay for it) building multiple massive research and manufacturing worlds early on makes it hard to target the spending since the money allocated to production gets divided around your whole empire.

It is tempting to fill every space on a planet with stuff, but trust me, only build what you need.

Last but not least, watch your relations with the other races, if you see one starting to dip and you can't risk war with them, send them stuff to be friends. Aside from certain random events (radicals assassinate one of their leaders and i get blammed for example) I have never been attacked without warning. Military is expensive early one so avoid building one as long as you can.

It seems like you're possibly making colonies too fast-each colony has a maintenence fee, so if you get to the point where that fee exceeds your tax rate you're really screwed. Dont lower your industry slider if you can help it... even going into the red (-500) and popping back up is probably preferable.

I'd also say you want to specialize your planets (research, factories... etc), and most ppl like to use big ~20 size planets as people farms - like 3-4 farms+entertainments, rest markets (enough factories to get going too).

Losing like 80 bc a turn isn't too bad, just try to absorb the cost, with a skipped turn every so often to go back up from -500. Eventually, if your approval is reasonable, your pop will catch up and your income will go up.

As a last resort-- consider starting with full econ bonus and be a federalist