I really can't help you with which units you should select but I can give you a bit of a heads up on the armies you listed.
Tourney wise, the Empire will be your most competitive with the War Alter/Steam Tank combo. The Tomb Kings, while not top tier, are close and can be a very fun army to play. The TKs don't have the offensive power of the Empire, but they don't suffer most of the weaknesses (moral issues being the biggest problem in the Empire army) either.
Skaven are kinda hurting right now. The 7th edition rules for skirmishers and independent characters has negatively altered the way that Skaven play. While Skaven can complete at local tourneys and do well, I doubt that they could do as well at national level tourneys.
You'll get more bang for your buck with Skaven or Tomb Kings, since they've started charging 22 USD for 10 Empire State Troopers, but that being said, I agree with Hesph- the Empire is definitely the army to look at these days for all situations. Gorgeous models (though not as pretty as the High Elves) and very mean on the field. The detachment rule is just downright abusive, too-- you can let the mother unit of two detachments get charged, and then bear trap them and have the two detachments on either flank swing in. Arm the detachments with halberds and you can go toe to toe with most stuff thanks to the handy +1 strength a halberd gives. WS4 Swordsmen aren't a bad choice either, but I've found they work better as the mother unit for detachments. Another neat trick with detachments is to have the detachments be a ranged unit... say, both crossbowmen. Detachments can stand and shoot when the mother unit gets charged. You can gun down a fair few models doing that, and let the mother unit handle the rest.
Then there are the War Priests and Greatswords, both of which are downright mean... flagellants are exellent if you want a firing line since an enemy has to kill every single one of the stupid buggers before they can break through, which gives your guns more time to shoot.
Wouldnt say you'd be getting much of a skaven force for under a hundred. You need @£%& loads of models in your army, especially if you want to field multiple units of the skaven's best troop type: Slaves (yes you read that correctly, slaves!)
You need a unit of clanrats for each slave unit, and since its barely worth equipping your rats with anything...even with the plastic kits, your looking at an expensive proposition.
All 3 armies can be quite competitive when played properly. It really comes down to which models and fluff you like the look of best and who's fluff you like best.
Empire - Empire can do a bit of everything. Magic, hordeiness, cavalry, shooty, war machines, ect. They are one of the few armies that have access to all 8 'standard' schools of magic. They usually will rely on weight of numbers and combat resolution to win battles rather than trying to kill large amounts of enemies. One of their main weaknesses is their average leadership and their overall averageness. A fairly easy army to get the hang of.
Skaven - Great army if you want an insane amount of rats fighting for you. Skaven armies typically have insane amounts of models in them, so if you play them, be prepared to do a large amount of painting. Skaven excel in Magic with their special lore, at shooting, and in dirty tricks (poison ect.) in general. The main weakness is their very low leadership, which is helped a bit due to the fact that for each additional rank of troops they have (up to 3) they get bonus leadership. As far as I know, Skaven have a mid level learning curve.
Tomb Kings - Undead Egyptian Skeletons. A very weak looking army on paper that relies on its amazing magic and overall teamwork to smash its enemies. They excel at controlling the game through their magic phase and using it to enhance their other game phases. They have a fairly steep learning curve, but can truly be a nightmare to play against in the hands of a good general.
I've never played with Empire or Skaven, so my knowledge of the 2 are limited, but if you need more info on Tomb Kings, I'd be glad to talk with you on chat or leave a more detailed post later . Good luck with your choice.
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