The Khwarezmid UHV is not too difficult, but still very entertaining to do. Both UU and UP are very powerful IMO. There are different strategies to accomplish the 3 UHVs, which have a synergy like for no other civ in SoI, apart from the Ghorids, maybe. They are:
- obtain 5 silk by 1230 - which means you'll need one small military campaign at the beginning, because you can't acquire the resources by trade and you don't have enough of them in your core area
- never lose a city to barbs before 1350 - which essentially means you must survive the Mongol incursions between 1220 and 1250 unharmed
- claim the title of Shahanshah - conquer the respective provinces. Basically, it's mopping up after the Mongols. If anybody can do it before 1250, that would be tremendous.
Once you spawn (and eventually change your civics), look at the starting situation. In the current version, the Samanids usually survive the 10th and early 11th century barb incursions and own up to three cities in Sogdiana. If they did keep their capital at Balkh, all of them will flip to you, which is great, for they are production powerhouses. Sometimes they move their capital to Bukhara or Samarkand, which does not flip and is your first target in this case. The city setup of the Seljuks, however, actually determines your early game strategy. At sultan difficulty and above, they have usually already found one city in Western Khorasan. If that city is Bastam, you might want to use one of your intial settlers to found Mashhad (which is better than Neyshabur in this situation because it's more easily defensible against barbs - you can bribe Alp Arslan into opening borders right away), but if they found Neyshabur or Mashhad, save the settler - you're going to take Khorasan from the Seljuks by force.
But the first thing you want to do is wipe the Samanids off the map. Your intial units will usually do for that. After that's done, build up your production capacities and economy and count your silks - you have two or three (2 near Samarkand and Balkh and 1 near Otrar or Mashhad, depending which city you found). An additional one can be obtained by conquering Kashgar, but that's ahistorical and results in a big economical and stability hit - you will take the rest from the Seljuks, because the other silk resources in your vicinity are in Eastern & Western Khorasan, Jibal and Kurdistan. Build up a decent army of trebuchets, UU lancers and archers to defend your conquered cities. If you went for Otrar earlier, you only need to secure Khorasan (except for Herat, which is only a drain) - if you didn't you need to take the fight further into Western Iran, which is quite feasible, still not advisable because all you want is to deal a quick blow to the Seljuks and get the silk before the Mongol invasion. Don't overextend. If you're lucky, the Seljuks have already overextended themselves and collapse around 1200, otherwise they succumb to the horde anyway. Make sure you have 5 silk resources hooked up before 1215 because the Mongols will most likely pillage all of your tiles.
Speaking of the Mongols, they'll fall upon you from 1217 on, so while fighting for the silk, you'll seriously need to prepare for their arrival in the mean time. You do this by researching the very useful techs of guilds (for Marksmen) and castle building. On sultan difficulty, it's possible to get both in time. But you really only need one of them. 4-5 marksmen behind castle walls hold off the onslaught comfortably. You can compensate for the lack of castles by building more marksmen or compensate for the lack of the guilds tech by putting a lot more archers into your castles. Dig in and hopefully the pillaging of the horde does not break your economy too badly. The Mongols come in two waves, hitting your core empire during the 1220s and Western Khorasan again during the 1250s. Once the Mongols are gone from Sogdiana and Eastern Khorasan, move all your excess city defenders westwards to unite with the army left from your campaign against the Seljuks. Use all of those troops in your quest for the Shahanshah title - you don't need them at home any more, but they can conquer and garrison new cities.
You don't have a time limit for the title UHV, but you may want to do it until 1370 the latest, when Timur shows up. If things go well for you, you can even make it before 1350, when the barb UHV triggers. The Mongols usually will have razed a couple of Iranian cities, so use a cavalry unit to scout ahead and build the necessary settlers in time. Sometimes Oman gets into Fars, but are not a problem to kick out. At some point you may want to switch to the empire civic and tech for civil service to maintain stabilty and economy.
Happy empire-building!