Greece and the Celts are our favorite civs. Rundowns on those are greatly appreciated.
With civs with a very early melee UU like those two (also Aztecs, Persia, plus Zulu due to their UA and depending on map Songhai and Carthage as well) I found focusing on Tribute as the early game (pre-t100) main source of yields income pays off very well.
Mining -> Bronze/Pottery -> Whatever (work toward upgrading your luxuries and unlocking your UB)
Monument -> Shrine (if you're Celts or Aztecs can skip it for now and get one extra UU, if you're not then forget about founding and just pick God of all Creation) -> (Well if available) -> UU spam. If there's no Rome/Zulu in game (due to their love for a Bronze Working beeline) and you have decent production/nearby Mercantile CSs then try fit Statue of Zeus. It usually doesn't go before t45 on Deity, ymmv.
Authority into Tribute, then Dominance (be sure to already be at war with a nearby opponent or two to milk science) and finally Imperium. Don't be tempted by earlier Imperium and settler spam, that's only going to delay your teching and you need to invest all your resources into early game bullying.
Remember: supply cap is just a number.
When you only have one city and don't care about growth (no granary/aqueduct/council, not enough good/improved tiles to work) you only miss on production but can make up for that due to overwhelming military prowess.
I ask for gold to maritime/religious CSs, or to any other CS if it means saving 3 or more turns of walking into their direction with enough soldiers to extract an heavy tribute. All that gold goes into upgrading warriors/rushbuying spearmen, ignoring the supply limit. Mercantile CS production also goes into soldiers, or a key early building (SoZ, stoneworks, forge, watermill...). Cultural and Militaristic CSs are your best farms, especially if you lack a nearby sucker to bash (barbarian farming alone is not enough to justify Authority), but be sure to have an army WAY bigger than needed due to military ranking fluctuations.
Notice how I moved war to the least juicy target (some crap and rather distant Hunnic cities rather than Delhi) because that let me move my army right in the middle of a CS cluster. That means tribute is possible every 4-5 turns. Once I approach Imperium I start work on settlers, then conquer and raze those low defense expos and fill all the wasteland.
Drill on all units, exception if your opponent is spamming spearmen as well, or you're Persia (because marching Immortals are just groovy). Then if you're facing some heavy archer spam go into cover, else work toward t3 promotions. The idea is, you're overkill against no-UU/no-Authority opponents, it's just cities slowing you down and without drill even wall-less cities with a garrison take too heavy of a toll to be conquered before siege engines. We also don't want archers/siege at this stage of the game, due to their low combat strength for Tribute purposes.
I can't help thinking in this game I could have gone even more nuts with Hoplites and spam some more to extract tribute from a couple of more distant CSs, anyway you can see supply limit not being an issue anymore once you start fill the land, and it only took 10 turns here:
Despite no science/culture CS tribute I'm first for # tech and tie for #policies on my continent and 3rd Literacy overall. Time to settle down and build some infrastructure, those early UUs are great to put you in a winning position but won't carry your military for much longer.
Don't early settle cities like this until you have the army to back it up or the city is in your backyard. Even with a good army, defending such a place that is on the enemy's border is just asking for lots of trouble.
