sbc said something important in the fact that you just can't counter everything. What you do want to try and do though is make sure you have answers to the common threats. You yourself can capitalise on this mentality by using lesser known threats: Sure the general sweepers work great, but sometimes having that one niche, unsuspected Pokemon can net you the win. It's still important to recognise what has potential and what is just a gimmick or purely outclassed.
Priority is important as well, an even spread of priority across a team decreases the chance that you'll be swept by <insert random set up sweeper here>. Speed tiers are important to learn as well, although the main ones would be learning the speed tiers of different scarfers, and what reaches 19 speed and what doesnt, as well as the big three that reach 20- Elekid, Voltorb and Diglett.
As for help, the Little Cup Big World article is still helpful even though it is a trifle outdated with the ban on Misdreavus. #littlecup on the synIRC server is where you'll find all the Little Cup people, and even the CAP server is good for asking help, only when its active though.
So in general, pickup a team, start playing a few matches, and the game will come to you in no time. Have fun with Little Cup!