How to play a "crazy" character?

For our next dnd game, I'm thinking of focusing more on role play than pure power. I'm usually the only min-mixer at the table, so I thought to try something different.

The character I'd like to play is the wise fool or mad sage archetype, someone who acts crazy and nonsensical, but beneath it all there is some deeper wisdom. Think the Ice King from Adventure Time or Kinger from Amazing Digital Circus.

Looking for some suggestions on how to best play this character without being too out of pocket or too weak (again, role-play was never my strong suit).

Also, any thoughts on the build itself would be appreciated. I was thinking a Paladin, but idk.

Thank you and wishing you all a lovely day!

Determining how to play is all based on where the line is that you do not cross.

Finding that line is difficult, and be open to backing off if someone complains.  You also need to learn to read the room.  If you can't read the room, then don't do it.

I assume this is a physical interaction and not online.  Being online makes reading a room more difficult and people read your text differently then intended.

I assume you are asking because you don't actually know anyone with mental issues, make sure your party is all ok with your concept.  By them knowing can mean a little acting goes a long way and does keep the line a safe difference away.

It sounds less like you're trying to play someone with a mental illness, and more of a silly, zany type. I hope that's the case because playing someone with a mental illness (especially if you are unfamiliar) is a minefield.  Are you looking for someone who acts similarly to Elan from Order of the Stick, perhaps? When I hear "acts crazy and nonsensical," I hear "Bard", not "Paladin".

One notable problem I see is the "beneath it all there is some deeper wisdom" part. That's the kind of thing which works in scripted productions, because they're carefully scripted. A TTRPG is improvised by definition, you have to react spontaneously in the moment. If you don't already have the improv skills to be able to improvise "zany on top, wise under the surface," you're only going to end up hitting the zany part and missing the "wise underneath" parts. Since you've already said roleplay is not your strong suit, I would strongly suggest you consider trying something with a lower degree of difficulty.

Yeah, "wise fool" or "mad sage" don't really work without the advantage of their actions being curated by the omniscient viewpoint of a writer. Especially if you're going to have them outright act disruptively- unless you're in a long-time group that's comfortable with the idea of you pushing boundaries like that, trying to play this out is more likely to just aggravate other people at the table.

As others have mentioned, it's difficult to be a stupid and smart at the same time. Maybe you can "tone down" the craziness into a simple characteristic quirk? Such as being stubbornly curious about how potions and how different reagents behave when mixed and even when the materials make no sense mixing (like mixing rock, paper, and scissors)? Or maybe they're uncontrollably determined to look into sarcophagi because they've heard of a treasure? Maybe they adore scones? Something where people know that the character is a little... odd, when it's about random exploration, but is reliable when things get serious.