There is a monster list which is broken into two rarities. Most monsters are common and every specific one has the ability to rise in tiers and ranks. There are limits to some monsters ability to reach a certain tier and rank. The lowest being tier 1 Rank E and highest being Tier 100 Rank S. The monsters tier and rank usually aren't decided until they've been tamed though. [@KingOfTheSkies]

Hm. Make a character, choose three monsters and see if you are accepted. >_> Oh and..
You essentially choose where to go and what to do and as you go along events will occur that you may or may not choose to follow. But for every place you wander to (or are directed to) you will run into possible quests or dialogue. It's a learning experience overall and is very character driven. However your character growth is up to you so use your freedom in this world wisely.[@Mae]

Battling monsters will not be the only reason to have them as you travel through this mysterious land. I will update the second post with the monster list in a second.