This for achieving 100 000M in a single game.
I'd recommend USA to start as it periodically grants you 500 every few sols.
The best way is definitely research for money.
*New Edit* The developers patched in a cost increase for continually researching the Martian Copyrights and Martian Patents. However I still believe them to be a strong starting point for gaining some cash quickly before investing in using Mohole Mine and mineral export below.
I don't know exactly how any of the values below have also been adjusted since this guide first went up. Don't know if the max science output I had is still accurate or possible. *End Edit*
The Martian Patents - $500 for 3000 research is more efficient then the Martian Copyrights - $2000 for 15000 research.
Martian Patents is $2500 for the same 15000 research spent.
You can easily tailor your colony to research, there are diminishing returns on additional Science Institutes and Research Labs. I believe any more than 5 of each becomes a net loss.
3 of each, all fully upgraded, staffed with a mix of scientists and no specs, in a mega dome with a Network Spire, plus the Omega Telescope, will produce about 10000 research total per sol. That's $1500 per sol.
One of my colonies with all wonders and techs produced 20000 at its peak (3 labs + 3 Institutes) due to all the additional character perks, genius colonists, and these two breakthroughs;
Superconducting Computing turns excess power into research at 1:3 (700 excess power = 2100 research).
Zero Space Computing gives another upgrade to Labs and Institutes (25%)
Obviously you can add to this by exporting any excess rare metals. Mohole Mine produces 20 per sol, and you can place multiple extractors on a single deposit. You'll need a steady supply of rockets and fuel unless you have the elevator, which can export 100 rare metals at a time.
There's also an additional breakthrough that allows extractors to function without colonists, but at 50% max output. Which means you don't need a dome at every deposit.