If you wait until the 3rd ruin for population, you can't take it again until the 6th ruin, and that's too late in my experience to time it. You might not even see 6 ruins in early scouting. I think population, culture, technology is probably the best order for Liberty. That first population ruin often lets you work a bonus food tile + hammers to speed up your Pathfinder and Monument builds.
Your other advice sounds solid though thanks!
I see your point, but, here's how I think of it. pop1-pop2 is between 5-8 turns. If you have a 3-food tile to start (which you almost always do as Shoshone) then you're at pop 2 on turn 5. If you take growth on turn 2, you've saved 3 turns. This makes it a waste.
So, I either take population right after I hit pop2, and hope I get another, or I wait until pop3 to take population.
My three possible orders are:
1) culture->growth->tech->CB upgrade->growth->tech
2) tech->culture->growth->tech->CB upgrade->growth
In both cases I replace #5 or #6 with faith depending on what turn I get the ruin.
This does mean I don't get a second growth ruin unless I get 5 ruins, yes.
Other notes:
* If I find a ruin on t18 or 19, I wait until t20 to claim it to ensure I get faith.
* Sometimes I'll ignore the ruin closest to my capital until my second pathfinder spawns, if it's in a spot where I'd see the AI coming before they got it, so I can keep it around as an ideally timed growth or faith ruin.
* Speaking of ideally timed growth ruins... I'll wait a turn or two to claim a ruin if my city is about to grow.
If you have really good production tiles to work, (like multiple 2hammer3gold gem mines) it can be worthwhile to stagnate at pop3 and build a settler, and rely on a ruin to get you to pop4. The ruins leave you at the same overflow amount, which, after growth, is a much smaller percentage of stored food needed to grow. Plus, you typically don't have enough 3-food tiles to keep the momentum going.
Thus, a growth ruin halfway through growing typically leaves you much farther from the next growth than where you started. (halfway through pop2 might turn into 1/4 of the way through pop3)
So, by stagnating and relying on a growth ruin to get to pop4, you get a settler out super-early without significantly affecting growth. (IMHO)
But, this heavily relies on a ruin to get you from pop3-pop4. Which is why it can be worth saving one. If you get lucky and don't need it for growth, you can spend it on faith.
I even consider buying a pathfinder if I get enough CS gold early. (build one, buy one for a total of 3) Normally it's not worth it, but every ruin you find with Shoshone is worthwhile. Considering that you can get extra free techs, or multiple CBs, it's *totally worth it*. Would you spend 220g on a CB? Heck yes you would.
Lots of fun ways to tweak the Shoshone start. It's flat out OP if you work it really hard. Having two CBs 40 turns early is... yeah.