based on your current stats, i would say all except level. only boost level when you need it to train the other stats at the training centre.
my preferred training order is health > str > def/speed > level (when needed) and repeat. you could train them in any order you want, it's totally up to you!
a complicated answer would probably confuse you and of course i wouldn't want that haha.
also remember to do shinwa's quest and get your pets a job for a chance to get stat boosters/stats. (:
for your current stats, basically all stat boosters are good as long as they're at a good price. you could try to avoid ones that increase levels since they will bump up the prices at the training centre but it shouldn't matter too much since you'll need them sooner or later anyways.
Don't forget to do battle quests every day! The experience you gain can be used to buy any stats and is cheaper than buying boosters.
How you train is completely up to you. Understanding what each stat does and how your enemy uses that against you is important. Health is straight forward. Defense and strength have a formula to them and are tied into damage dealt and damage defended. If your pet has 1,000 strength that does not mean he will do 1,000 damage. Speed is related to crit hits. If your opponent has higher speed than you, he has a chance to do double damage. If you have higher speed than your opponent then he cannot crit you. Speed and strength work together while defense and health work together. How you train these stats is completely up to you. If this is your first battle pet, it is best to train evenly for a little while until you decide what you would like as a final build.
I was actually wondering the same thing. So basically all stats count so train all of them until you get very strong. I need to remember to do shinwa, I always do other quests first and then cant complete hers.
You don't have to train evenly until you are very strong, although some people do choose to train stats evenly until they hit the cap. As you battle more opponents you start to get a feel for what stats you would like more of, depending on your weapons and battle strategy. It's easier to boost one or two stats when you are training all of them instead of boosting one stat from the beginning, only to realize you rather boost another stat that is very low. Boosting also means that you will only be able to train that stat with boosters unless you boost level as well. If you boost level with one of your other stats, then you can still train that stat in the training center. However, the cost and time it takes to train your pet in the training center goes up every time you increase level a lot.