Nothing brings pleasure into my cardboard trading card life like applying multiple layers of plastic to seal them away and provide some lovely thickened shufflefeel.

Also, nothing fights against foil-card-curl like a sleeve. Aside from some very intense and specific control over humidity.

Here's my own sleeving solution:

Battle Cards
These are Standard-sized cards (the same size as Magic & many many many other games), so you have a few billion options at your disposal. Personally I am a fan of Ultra Pro Eclipse sleeves for their particular shuffling handfeel, especially when I decide to be a pervert and double-sleeve with KMC Perfect Fit inners.

Character Cards
This can be less easy. The main thing to bear in mind is that you'll want sleeves with dimensions around 3 x 5 inches. Some options folks have found include:

• Mayday Games sleeves for Tiny Epic Kingdoms. The 100 counts are somewhat soft, close to but not quite like your classic penny sleeves. The 50-count Premiums are a little stiffer and denser, and probably the most solid choice for a single sleeve.
• Ultimate Guard Precise Fit Sleeves for Oversized Cards. These aren't actually all that great as one-off options, as they're VERY TIGHT and kinda hard to apply. Also, they're incredibly slim, moreso meant for double-sleeving as an inner sleeve. Which I've done in conjunction with either type of Mayday sleeve. The Mayday Premiums are kind of...Dragon Shield-hard to double-sleeve, but I've done it and feel incredibly self-satisfied.
• Toploaders. There are 3x5 ones out there (I think by BCW?), while I myself have been using 3 1/2 x 5 1/8 Ultra Pros. These seem to be the top pick for anybody storing their cards in stacks or boxes, and still are worth having a handful on-hand for gameplay even if you're using a binder solution. Also, you can join me in the decadence of taking a double-sleeved character card, plunging it into a toploader, and wielding the unstoppable power of a rock-hard triple-sleeved character card.
  
• 4-pocket Binder Pages. Ultra Pro do some of these, which are a great way to store character cards in a fancy manner. Double-sleeved character cards fit in here, providing a kinda-sorta-fake way to say you're triple-sleeving them. Toploaders do not fit, so I am denied quadruple-sleeving. For now.

 

Someone on the facebook TCG group put Metroplex into a thick magnetic acrylic frame meant for photographs and I KINDA WANNA DO IT NOW

 

The upside of toploaders is you can straight up rubber-band them together with no risk to the actual cards. As for actual cases, the Ultimate Guard Arkhive or Quivertime's Quiver are the two I have that can hold them easily.

 

They can go in standing just like the deckboxes, according to UG it can hold around 175 of them