I think a lot depends on your definition of REXing? Imo a REX is nothing less than expanding to the point where you have your research slider at zero and are bringing in negative, yep, negative gold per turn, or close to it. After all, we are talking about a RAPID expansion, otherwise you're simply settling your land, blocking, and bringing your research/tech back up for a second settling wave later.
The other half has to do with what level you play. Imo levels such as Immortal/Deity don't allow for an all out REX, say where you have settled 10 cities around 1000 (IMP) - 700 BC range (normal speed).
IMO a REX should follow something along these lines:
Early focus should be on Libraries and running scientist to fuel research. During a true REX cottages should be minimal because they serve nothing more than gold which will cover your maintenance cost, along with gems and gold mines (if they're available). Fail gold from Wonders is another great way to get gold, especially with stone/marble or any Industrious leader, Although I prefer CRE for ideal REXing.
During a REX the emphasis should be on land grabbing so you should prioritize techs like Writing for scientist, Alpha for building research and trading (scientist help you reach Alpha fastest, barring an Oracle slingshot), and Currency (at which point all your problems are solved) for building wealth, +1 trade routes, and of course, selling techs for cash.
Another great thing about scientist is they allow you to work fewer tiles while still bringing in pure beakers to fuel research which is very important. This is huge imo because its really important to grab and settle the land first. If you make too many early workers you end up delaying your settle spam.
A nice leader to practice REXing with is Cathy. IMP is great, especially when paired with CRE because it allows you to quickly produce/chop settlers from your Capital and run 2 scientist. It usually works out like 7-8 turns per settler
with 2 scientist and 3-4 with chops (2 workers/1 chop each). You're second city should also be a settler pump, while you're 3rd city can work some scientist. Settle the 1st GS in Capital. A great initial build for Cathy is to research a food tech, then BW while queing a warrior, grow to 2 pop then directly chop a settler and one worker. One worker improves at home to happy cap, chops another worker, Library, runs 2 scientist, then begin chopping (kill all the trees!!, lol) 5 settlers. The other worker (2 pop) follows your settler. The early founded city grows to 3 pop and begins settler pumping as well. 3rd city can run 2 scientist while you're 4th city and beyond can concentrate on making workers/units.
The key is to put your slider to zero after you've researched Writing and once you have 2 scientist in your Capital go to 100% until Alpha is finished, at which point throw the slider back to zero,
accumulate gold (you'll need it), and use scientists (and a settled GS) and building research (new cities, even at 1 or 2 pop with no improvements help) to fuel research to Currency. When using this strategy with Cathy on say Monarchy, you'll normally have 10 cities by around 1000 BC, a zero research slider, and typically
negative 15 - 22 gold per turn with Currency anywhere from 4-8 turns away (I usually grab it sometime in the 800s).
Imo the key tech is Currency and the quickest way to get there is via scientist and then scientist/building research. Food rich cities can run scientist, work cottages, and grow while production cities that aren't making more settlers/workers/units build research. You should be able to gain enough happiness resources to skip Monarchy until you can trade for it which lets you be a little more flexible with tech choices after Currency. Besides, with a huge land grab comes lots of luxuries not to mention alpha which allows you to trade your monopolies for the luxuries you need for more happiness.
What I think are key points:
1. Scientist are your friend
2. You can never chop enough
3. Lower
initial worker count (3) actually helps fuel you're REX
4. On Monarch and below you typically don't need Chariots/Axe/or Archers and on most standard size maps your settle spam plus AI do enormous amounts of fog busting allowing you to save hammers for initial units.
5. Hunting/Mining Leaders work best (and most are CRE, yay!) because they allow you to work a food source and directly chop,
and, they also allow you to
bypass the WHL and POT, so you can tech through AH, WRT, Alpha, where you can then backfil. You absolutely do not need a single cottage nor granary till that point anyways and unless you're playing on Emperor, you don't need roads yet either.
6. Infrastructure: IMO its best to beeline as quickly as possible to Currency, therefore, unless you're an EXP leader such as Sury, I would delay granaries in every city (at the very least most of them).
The key is to balance having enough gold so you can deficit research Currency. If you can squeeze in a few granaries via the whip and retain balance then go for it but in my experience, unless you have 2+ gold/gem mines, you need to delay granaries. Besides, the key is to go horizontal and mass land grab. Once you hit Currency you can focus on going vertical.
Hope this helps the OP!! If nothing else it can serve as a general guide that can be incorporated into other leaders as well
per city to grow them larger.
