Important Stats to Raise and Why
Every Monster has different main damaging stats, either Strength or Intelligence and depends on either taking hits or dodging all hits. You'll have to pay attention to how your Monster is played first and foremost, the one I am using as an example above is a Monster that's good for dealing heavy damage while dodging attacks.
It has increased stat gains in Speed, Power and low stat gains in Life, Int and Skill. There's a great guide over at Gamefaq that goes over each Monster's innate stat boosts, I won't be covering that info here but you should take it into advisement when leveling up a Monster. I also recommend you read parts of that guide as it has a bunch of great info.
If you don't already know this, during Monster Rancher your Monster will go through a life span, starting as a Child then moving on to an Adolescent then it'll hit its Prime before eventually dropping off and becoming Old. When it's a Child and an Adolescent, it'll receive regular stat gains. When it's in its Prime it'll receive significantly higher stat gains. You can tell when your Monster gets older as it grows bigger in game.
To increase a Monster's stats as much as humanly possible during its life time you'll want to do nothing but run Drills during its Prime, you'll also want to do all errantries during its Childhood and Adolescence. Never do an errantry unless you're getting a Tech and never do an Adventure unless you're building your Monster just to do that.
Now, with all of that out of the way, depending on what you want to do with your Monster determines which stats you want to raise. Here is a quick run down of the stats and what they do.
What the Stats do in Monster Rancher 2
Life: Determines how much Life you have during Battle and how much Energy you have on Adventures
Power: Increases the damage done by Power attacks; also determines how much Energy you have on Adventures
Intelligence: Increases the damage done by Intelligence Attacks; also determines how much Energy you have on Adventures
Skill: Increases your Monster's chance of hitting its opponent
Speed: Increases your Monster's chance of dodging an opponent
Defense: Decreases the damage you take from all attacks
For those of you looking to Battle with your Monster you'll want to primarily focus on your main damaging attribute (Power, Intelligence) and Skill. This will allow you to deal heavy damage and hit your opponent. Secondly you'll want to focus on either Defense or Speed. Whichever one your Monster has higher stat gains for, that's the one that I typically run.
If you're looking to raise a Monster that's going to do a bunch of Adventures I'd recommend you pick a more well rounded Monster like Mocchi. A Mocchi isn't the best for combat but they live pretty long and they have good stat gains in Life, Power and Intelligence.
Almar's Favorite Battle Stats Quick List
Life: 4th favorite; Life is good but Defense is a better defensive stat.
Power: 2nd favorite stat for Physical damage dealers
Intelligence: 2nd favorite stat for Intelligence damage dealers
Skill: 1st most important stat; this stat determines whether or not you hit your target, you can beat the game with a Monster high in a damage dealing stat and Skill guaranteed.
Speed: 4th favorite; unless your Monster has higher gains in Speed than Defense I get Defense primarily instead
Defense: 3rd favorite stat; Battles are determined not by how much HP you have remaining but the %.
I prefer Defense over Life because I feel that reducing the size of the hit helps you more than Life when Battles aren't K.Os. Typically once I get over 600 Defense no enemies hit me for more than 30 unless they're lucky and land a devastating blow that does 70 - 100 damage. Devastating blows only happen about 10% of the time I am hit though.
On the other hand with high Life and no Defense it feels like every hit is a devastating one. This is just my personal anecdotal evidence from playing the game. As for my other stat choices, if you read around on the internet you'll find that almost every Monster Rancher 2 guide unanimously agrees that Skill is the most important stat along with Strength or Intelligence. Typically Speed, Life and Defense are argued as third most important.
Almar's Favorite Adventure Monster Stats Quick List
Life: Determines how much Energy your Monster has
Power: Determines how much Energy your Monster has and how easily they can destroy obstacles on adventures
Intelligence: Determines how much Energy your Monster has and how well they can find hidden routes on an adventure