Here's some general advice that I have, learn to live without Nana, although she gives you tools, having a good Sopo is half the battle. The first few posts on The Ice Climbers General Chat talk about a few Sopo combos dthrow nair, bair, and I'd recommend understanding Sopo know his moves, movement options, and percents (you won't find that online it hinders just as much as it helps). There's also a Maining Sopo thread that has some useful info.
Here's a quote from Wobbles when asked how to get good with Ice Climbers "Learn how to wobble. Then stop wobbling. Then start wobbling again." then he said something along the lines of then you'll have an unbeatable punish and a neutral to back it up. That being said Wobbling is an important component of the Ice Climbers' game, knowing its limits early on will help you out in the long run, but using it as a crutch may grant you wins against low level players, but against players with IC knowledge they'll kill Nana in 2 hits and you'll be stuck with Sopo. I'll have an interesting thread on wobbling later (after a new tech thread that I'm currently working on).
Ice Climbers are unique the way Wobbles and Chudat play them are quite different. Understand that they're a hard character to master and you'll have to compensate for their flaws. Like with any character the best way to get things down is to grind and there's a ton of tech just for the Ice Climbers, so expect to grind a lot.
At tournaments expect people to counter pick them with Peach, Fox, or Samus. There are guides I'd recommend reading.
If you want an easy character I don't think it's Ice Climbers...
Other than that, up air is your friend, dsmash comes out frame 6, and DI/aerial drift will get you far.