I'm creating a new character, a fighter.I'd like to join House Hlaalu as a warrior this time, but why would warrior who's not interested in business and black market join it? Just trying to RP when there's nothing else to do.

I assume you're a member of the Fighter's Guild... or will be.
Hlaalu's the house most open to Imperial influences (like the Fighter's Guild). So you could've overheard your FG chums saying "Oh Hlaalu's great, they aren't as xenophobic as the rest of them!" Or something like that.
Why do YOU want to join Hlaalu with a warrior anyway?

You could RP that your character was born into House Hlaalu. Pretty much all my characters that were part of House Telvanni were born into the House.

They are the most open to outlanders so it would make sense in that way. They are also rapidly gaining power and influence over the other Houses so if your character is interested in such thing House Hlaalu would be the best choice.

Also, the fighters guild and Hlaalu are deepy linked.....if you choose a certain path in the fighters guild it makes complete sense to join Hlaalu.

You can also consider yourself some sort of enforcer/man-for-hire at first. Some quests do involve fighting and for the more speech-related quests, nothing stops you from using force.