Okay so is Monster Hunter basically just an action/adventure-semi-MMO thing like PSO, just killing big monsters and loot whoring online with people?
Or is there like an actual story mode and stuff?
There is a bit of story but it's usually
incredibly fast paced and doesn't last you long. Saying this after still not finishing the storyline while having nearly 50 hours into the game is kinda funny.
Sadly in order to truly finish unlocking the Caravan Quests (Single Player) you need to get HR 8+ in the Gathering Hall (Where the multiplayer quests are.) You can go into them solo with your 2 NPC cats though but they have more HP then the Caravan (Single player) quests.
I'm at 86:55 time played with HR 3 and only 8 more offline quests currently available more will probably unlock as I finish them as well. There are 20+ more quests that unlock in the Caravan after you hit HR 8+.