I've played Tomb Kings for a number of years so i'll throw my hat into this conversation
I'm not very good at essays so instead i'll give you a brief description of each unit and what uses it has and how viable it is both in a competitve and casual enviroment.
Tomb Kings/Princes
Both varieties are amazing on paper with high strenght and toughness along with 1 more wound than most fighty champions and they give whichever unit they join their same weapon skill, either 6 or 5, meaning you can have skeletons with 6 or 5 weapon skill
Put them either on a chariot in a big unit and hope you break whatever unit you charge or put them into a horde of Tomb Guard.
The downsides are that they are extremely expensive for what you get, coming with light armour (no option for better) and having no good fighty weapons/armour within their own book so the vast majority of the time you'll simply give them a greatweapon, some armour and dragonbade gem because they're flammable. They have a special rule when they die that will deal damage to the enemy unit that kills them but realistically it never does anything and if he dies your unit will soon die after anyway.
You can also mount them on Warsphinx but don't ever try it unless you're playing very casually, not only will he just get killed easily by cannons but he also displaces ALL the crew and does NOT give his WS to the mount so all you'll end up doing is increasing the price of a warsphinx by 100/170 points with no gain in stats or survivability.
Conclusion 4/5, buy a prince (or a king in higher point games) and build him defensively because "a vampire he is not!" and stick him in a chariot/tomb guard unit.
High/Liche Priest
First off they're mandatory, you have no choice in the matter and if he dies your army will fall very quickly and horribly, awesome how the Vampire counts got a MUCH better version of this army crumble.
Take a lvl4 and give him the Lore of Nehekhara (mandatory for the highest level caster), give him Earthing rod and hope he doesn't failcast him self to death.
The army book lore of Nehekhara is generally speaking a "good" lore, it's extremely defensive and is generally used just to buff your units and make them less aweful, they also have high casting values with most of them being 9+ and the #6 spell is aweful.
Tomb Kings tend to have a very strong magic phase due to how many magic dice they can generate which is why you generally want to take another lvl 2 (or even lvl4) just so you can take an offensive lore such as light or death.
Conclusion 3/5, he's mandatory and can cast some decent spells, hope he doesn't miscast early or you'll lose.
Tomb Herald
Don't bother, he's weaker, has lower toughness, less wounds, aweful fighting stats and doesn't buff your units like a tomb king does.
conclusion 1/5, i have a nice conversion for a tomb herald and i like the hero thematically, realistically he'll do aboslutely nothing though.
Necrotect
He gives the unit he joins hatred and a single animated construct within 12inches 6+ regen, put him on the cornor of a Tomb Guard unit and don't buy
anything for him, hope he doesn't die before his unit gets to use hatred.
conlusion 3/5, think of this as a 60point upgrade to give your tomb guard hatred.
Core
Skeleton Warriors
They cost a point less than Skink Cohorts, come with a shield and can pay a point each for light armour and for spears.
Great fluffy choice, horrible gaming choice. They
will lose any combat that isn't grossly weighed in their favour by magic buffs and characters, you can't raise them any where NEAR as quickly as Vampire counts can and you cannot put a massively fighty combat lord like a vampire count inside them to make them win combats.
To make them win you need to buy a bare minimum of 50 models, 5 wide 10 deep and place a king/prince in there.
It's important to note that it's very common for you to lose 20+ models per combat phase through casualties and crumble and any other units in the same combat (such as warshpinxes) will instantly die as you share crumble with them.
Conclusion 1/5, you're honestly better off without them because they need babysitting while giving you no tactical advantage.
Skeleton Archers
HERE is the saving grace of the Tomb Kings core selection, at first glance they don't seem amazing with their BS2 and ordinary str3 bows. but once you play a few games with them you realise that with being undead (ironically one of the few instances this is an advantage) they never panic or run away and with the Arrows of Asaph special rule the will
always hit on 5s, even at long range against waywatchers in a forest in a building behind a hedge while wearing a camoflaging coat of camoflaging at night during fog.
hitting on 5's with str 3 seems bad but when you take them in significant numbers you'll see they can reliably whittle down big units and chaff, while utterly destroyed skirmishers, it's very common to take multiple large units of 20+ as core.
Important note; the Lore of Nehekhara has a magic buff called Righteous smiting which can make a unit (or boosted to a bubble effect) gain +1 attack per model and multiple shot (2) special rules, boosted in the middle of your army can easily turn your 40 bowmen into 80 shots per turn! and often gets 6diced.
conclusion 5/5, take at least 2 units of 20 as wizard bunkers and fantastic multiple shot archers.
Skeleton Horsemen
Low WS, strenght 4 on the charge and a 4+ save with vangaurd, these are reliable and cheap medium cavalry which tend not to get taken in most lists, if you could put a prince or king on a horse to go with these guys to buff their WS you could make a cheap bus of through at the enemy but for some bizzard reason kings/princes have absolutely no idea how to ride horses.
conclusion 3/5, a decent choice but suffers from lack of writers opportunity, basically every other race in the game can have fighty characters on horses and this would be a perfect place for a king to buff their WS.
Skeleton Horse Archers
Cheap and fast (for tomb kings) archer unit which can be used as an offensive horse liche priest bunker, genreally just used to kill warmachines with vanguard and fast cavalry rules.
conclusion 4/5, worth buying 2 units of 5 to kill/tie up warmachines
Skeleton Chariots
Completly unique to Tomb Kings you can buy
units of chariots, typically run as either 3 (for flanks) or 8-12 with a king on chariot as a main combat unit. In a unit of 12 these become scary with 4d6 strenght 6 impact hits on a charge, 12 strenght 4 spear attacks, 8 horse attacks not including the Tomb Kings attacks, all at WS6.
important to note, each chariot has 2 bowshots and with Righteous Smiting this gives EACH chariot 4 bowshots (if out of combat) or 4 extra attacks per chariot and 1 extra impact hit each. If you also buff them with Cursed Blades from the lore of Nehekhara they also ALL have killing blow.
conclusion 5/5, extremely good core choice, either take them in small units to secure flanks or make them big and add a character, scary unit.
That went on a lot longer than i originally planned it to so unfortunately i don't have time to finish, if you've found this useful i can write up the rest of the units and i hope this has helped.
