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.