This quest is incredibly difficult (at least for my playstyle) because you start with only 2000 gold with which to fight Saladin, the Sultan, and the Caliph, with only the Pig at your side. What is worse, the map is positioned such that your ally is farthest away from the action, and worst of all is the placement of the troublesome Caliph nearly adjacent to you. This map looks really scary but with some planning and a bit of luck it's not as hard as it seems.
My playstyle requires at least 3000 gold for what I would call a "safe and proper" setup but I've managed to tone it down to 2000gp for this and other missions.
You want to set up in roughly this order, going as fast as reasonably possible without messing up. Keeping calm is key.
Build Trading Post somewhere convenient and expand the stockpile by two or three blocks.
Buy wood until you have 250 or more. You'll also want at least 40-50 stone.
Place your Granary and immediately set it to 1/2 rations.
Build your Armory and Barracks. Buy 10 bows from the Trading Post and conscript all ten archers.
--NOTE: This is cheaper overall than buying Ararbian bowmen.
Build a square tower to the northwest towards the Caliph. Near your maximum reach there are a pair of boulders facing southwest+northeast. You want your tower directly below the southwest boulder. This may sound confusing; the purpose of this is for the tower to be as close to the Caliph as physically possible while out of reach of his Sentry Towers. This will give you maximum defensive coverage over your lands.
Build a single brick of wall on the tower so you can build stairs, and have all your archers get to the top, setting them to aggressive. Build two or three braziers so your archers will shoot fire and improve their damage output. These archers should harrass some of the Caliph's fields and serve as a good first line of defense against his archers, slaves, and horse archers.
--NOTE: Make sure your archers aren't targetted by his Arabian bowmen in his towers and vice versa. If they are, you'll be fighting a losing battle. Restart the mission if necessary and place your tower a little more down on the map.
--NOTE: Once your archers reach the top of the tower, destroy the bottom stair step so the tower cannot be climbed by enemy troops.
Now it is time to build the infrastructure of your setup.
Build two Apple Farms and four Wheat Farms to the east, on the Pig's side. We will wait on mills and bakeries for now.
Build three hovels somehwere out of the way (I actually build them in the center-east quadrant of the map; they are completely undefended but the Sultan will likely not atack them and if he does, hovels are cheap and easy to rebuild).
Build six-ten woodcutters nearby. You should be able to place a few behind your tower to exploit the woods to the west; nothing should be able to reach them without being in range of your archers.
Build two quarries with three ox tethers as well as two iron mines on the resources closest to you.
You will now be technically self-sufficient and should have some excess wood and coin, and should be able to breathe. The only thing you are missing right now is sustainable food production and a good defense.
Your popularity will be steadily declining due to half rations. Your people should soon be bringing you some apples and you have a little bread left. Buy 5-10 each of meat and cheese from the Trading Post. Having all four food types and no taxes will level you out at 0 Popularity change. Keep checking your food in the early stages and buy in meet and cheese so your popularity doesn't plummet. If you go under 50, go to full rations for a while or bribe your people under you're above. Sell stone and iron as needed to pay for wood or unexpected problems.
Make sure you have enough wood (or gold to pay for wood) in reserve to build a fourth hovel, a mill and four bakeries. I would not build these items until my wheat farms have produced some wheat in the stockpile, and I would try to wait for my woodcutters to bring me some wood so I don't have to buy. In any case, as soon as you see wheat, build the mill and hovel; once the mill starts making flour build some bakeries.
Your next problem will be your defenses. By now your archers have likely repelled a few Caliph strikes but you have another problem. You have no answer to the Sultan's strikes (your first tower has some coverage against the Sultan but not enough) and furthermore, your archers will have a hard time killing waves of arabian swordsmen.
Once you have enough stone, build another stone tower facing north towards Sultan. I would place this as far forward as possible, nestled into the jagged terrain. Place braziers and stairs. Buy ten bows, crossbows, and leather armor (you could try asking Pig for leather armor or crossbows, but in my playthrough HE is the one asking ME for these things) and conscript them all. Send ten archers and six crossbows into the second tower (the Sultan is more likely than the Caliph to send swordsmen) and the rest of the crossbows to reinforce the Caliph-facing tower. You will have to rebuild the bottom stair to do it but this shouldn't be a problem. Destroy both bottom stairs once done.
Now you should have a modest but adequate defense against all three foes and a good pile of wood. Time to go build happy! Build as many hovels as you need before building as many quarries, ox tethers, and iron mines as you can to take advantage of your resources. Build as many farms, mills, and bakaries as you need to become self-sufficient. Eventually the time should come where you can stop buying in food and going to full rations.
Build fletchers or buy in bows as needed to keep your towers manned. You should have roughly twnety archers and five crossbowmen in each tower to repel most attacks. If you can spare the money, feel free to build an Engineer's Guild and build some mangonels or ballista on your towers for more harrassment.
Now that you (hopefully) have a sustainable economy and defenses capable of repeling most attacks, it is up your personal playstyle how you want to take the offensive, as well as shore up your defenses. You might want to build walls and enclose your keep (during my playthrough Saladin did send a wave of assassins at me), but I prefer to keep selling off all my stone to fuel other endevours, such as keeping a ring of archers to guard all important buildings/resources.
Take the offense however you prefer, but start with the Caliph. He is the closest to you and the most likely to be a thorn in your side (excepting any swordmen waves from Sultan and Saladin coming north). I prefer building trebuchets close to my stone tower (for passive protection and so I know Caliph's archers can't hit them) and shell his Engineer's Guild (which can mess you up if he's allowed to build siege weapons), Mercenary Outpost, Trading Post, Granary, or whatever else looks good.
My approach was to troll him with the trebuchets and build fletchers, blacksmiths, dairy farms, and tanners
to produce bows, a few crossbows, maces, and leather. I build bows and crossbows to keep my towers manned (though if placed well few should die), and either buy in leather and/or sell excess maces and produce macemen. Once I've assembled a good force of 50-100 by trebuchets punch a hole through his towers/walls and the macemen finish him off. Do it however you wish.
Next, the Sultan should be an easy target. For me it was harder to build trebuchets/catapults without Saladin's archers interfering and attacking them, but a direct push of macemen took down the Sultan's walls rather quickly, and after a melee bloodbath I took out his Mercenary Post, Granary, Trading Post, and finally killed the lord with a few macemen left to spare.
Saladin is the last and greatest challenge, but by now you should be winning so finish him as you wish. I was unable to build siege equipment without his tower ballista killing them. Either find a way to barrage his walls with siege weapons, use tunnelers, or just make a full-out assault with assassins, maces, swordsmen, or whatever you prefer.
This quest is scary and your safety is shakey the first few minutes, but it's not as hard as it would first appear.