To add to the walkthrough post, I would always build the tavern first. I think military might is hardly necessary at the start of the game, and the Tavern increases your revenue, which makes building all the other shit quicker. If you want to infiltrate Raeve Keep with spies, I would only build the tavern as well (because the brothel is expensive as...dicks).
While it's true that the Tavern is a pretty good source of income, I would say that quickly bringing villages under your control through capture and trade agreements is an even better source—in my latest save file, at week 15, I have 97 gold per week coming from villages alone. Since there are more important research projects to take care of early if you want to infiltrate than there are building projects, my preference is to amp up the tech rate as fast as possible; and since I like getting the somewhat difficult Greyhide route started ASAP, my preference is to get the Dark Sanctum done first for the research, and the Forge done next for Greyhide. It also helps that getting both of those done first multiplies the effectiveness of each orc soldier, meaning I have to use fewer for capturing those early few villages.
That said, it's absolutely possible to get the brothel built in time for Raeve if you start with the tavern; I haven't tried it myself, so I'm not sure what sort of rate of money you'd get out of it, but you can certainly still get what I'd consider the four most important research projects done by Week 22 even with the base research rate. That said, if you can get up to a research rate of 15 or higher by week 12 (not a difficult feat if you start with the dark sanctum and are working with a map and can find abbeys quickly), you can get those 4 projects done by week 18 or sooner, giving you ample time to build everything if you can secure the funds—and if you can get to all 7 villages by week 10, you should have more than enough funds.
For reference, in that week 15 save file I was talking about, after building the Dark Sanctum, Forge, Tavern, and Brothel in that order, I'm sitting on 945 gold and have ~125 as my total weekly income (varying somewhat week to week), and I haven't even gotten at least one of the ruler events (the Cla-Min one triggered when I was trying to remind myself which research projects did what). Granted, not everyone's going to want to savescum the villages, because that's pretty tedious. With that kind of income, though, you can just build the Dark Sanctum, Forge, and Tavern in consecutive weeks and feel pretty safe that you'll have enough for the Brothel and the Week 22 quota as well, so you're only losing two weeks worth of the tavern's income. As to my preference for building the Forge before the Tavern, well, that's personal preference again, but the sooner you start equipping soldiers with iron gear, the fewer of them you need to capture villages, and the sooner you can start collecting money from them. I'm willing to waste another week of potential Tavern profits to secure those villages all the earlier.
tl;dr: Nothing wrong with going Tavern -> Dark Sanctum -> Forge -> Brothel, but I feel like it's more limiting to your options than going Dark Sanctum -> Forge -> Tavern -> Brothel. Speeding up those research projects early on really helps accelerate things, and you can secure pretty ample funds from villages if you know where to find them.
