Been a while since the OP started this thread but I'll throw in my 2 cents anyway.
Tomb King
-Destroyer of Eternities
-Enchanted shield
-General
Liche Priest
-Hieratic Jar
-Cloak of the Dunes
-Hierophant
Liche Priest
-Staff of Ravening
Liche Priest
-Collar of Shapesh
Pretty decent character set up. King - Prince - Priest - Priest is a more common set up, but both obviously work. I used to play TK and had a lot of sucess with the King with Destroyer of Eternities or Flail of Skulls and Cloak of Dunes (28" charge range) and 3x mounted Liches, 1 with the Jar, 1 with Plaque and 1 Herophant with either Collar or with the +1 to cast staff (If I used the Flail on the king I gave him the collar instead). Priests are VERY fragile so you want to play very defensivly with them, which means you will rarely be within 18" and in LOS of an enemy and thus never get to use the staff. The flying king can be extremly handy and flexible, but he lacks protection and if his My will Be Done gets dispelled he can get stranded in the middle of nowhere so you have to be careful where you fly. Perfect for picking up some pts later in the game.
20 Skelton Warriors
-Standard
-Musician
20 Skeleton Warriors
-Standard
-Musician
Im personally not a fan of the Tomb Kings skelletons, I much prefer the archers, hitting on 5+ is powerful, espeially against skirmishers, and with the shooting spell they can really dish out some pain. If you take skellies you want bigger units, they can't get raies above starting strenght and killing a unit of 20 skelletons in a single round of combat is actually pretty easy for heavy hitters. If these units are intended to be archers then ignore this comment.
3 Chariots
-Standard
-Musician
3 Chariots
-Standard
-Musician
-Warbanner
Great choices. Units of 4 is sagnifically more effecient imo, but its more a matter of taste and with 3 big fighting blocks on the table you will have trouble fitting too wide chariot units in your deploy anyway.
20 Tomb Guard
-Banner of the Undying Legion
You reeeeaaally want the Icon of Rakaph on these. It allows them to make a free reform
before charges are declares, which effectivly gives them a 360 degree charge. This is very powerful and makes it impossible for fast units to try and sneak past them. You can also reform, move 4" in any direction and then charge 8" with magic, which means this unit creates a (24" + the size of the unit) sphere of death, anything inside it risk getting charged by a unit of fighty Tomb Guards.
Tomb Scorpion
4 Carrion
4 Ushabti
Carrions are fantastic, they can move 12" away from your casters in the movemen phase then charge 20" with magic making first turn charges on War Machines possible, and very effective. Tomb Scorpions are another amazing choice, they are fantastic fighters, great character snipers due to KB and their tunneling rule where they can charge the turn the come up is great for taking out gun lines or support units. The Ushabti on the other hand are very cool looking models, but doesn't come close to the effeciency of a 2nd Scorpion. They are very expensive and pretty fragile with only T4 and 5+ save, and they don't really hit particularly hard either. Useful but far less effecient than the Scorps.
Screaming Skull Catapult
-Skulls of the Foe
Screaming Skull Catapult
-Skulls of the Foe
At first glance this set up might seem optimal but I found that the Bone Giant is a fantastic addition to the army as well. Moving 6" then charging with magic 12" makes the Bone Giant very fast, and as he breaks ranks and gets free pivots he can move 6" into a units flank arc then charge 12". He also hits pretty hard on the charge, but its his unexpected speed that really makes him good. The Skull catapults are good against big blocks of infatry, but they will struggle to make up for their pts cost against smaller armies with lots of skirmishers like the DE, WE and LM.
I want to work in a prince too, but are princes better than priests?
In a defensive, counter attack style list you need as much magic as possible to get magic shooting off in the beginning and magic charges in the later turns, and the Prince is very limited in what he can. In an offensive straight-up-the-guts type of list then a Prince on a Chariot of Fire wielding the Antrack spear is pretty good and adds a lot of offensive power. I've seen some players do well with a big unit of Chariots with both King and Prince in it (both on chariots ofc) but that type of unit is too easily wiped out by S7 attacks. I personally think that the prince is worse than a priest in most situations and that the TKs are better suited for a defensive play in the first 4-5 turns, then launching at the enemy with magic charges in the last 1-2 turns to pick up a lot of points or mop up whatever is left after the shooting.