Well level is important for sure as of course you can't train any other stats if your level is too low. Balanced stats are the name of the game when it comes to battling - HP, atrength and defense are all important. Movement is useless and has no power in anything on neopets.
Most battling pets either have balanced stats or they have a high HP and strength if they have been lab trained. If you are actually looking to dubloon & codestone train though then you need level, strength, defense and HP all kept up to speed. To train any stat you can't have any of your stats (strength, defense, movement, HP) over twice as high as your level, so you might need to train level first if that's the case

Dubloon training is cheaper to begin with though it takes a little longer - well worth the np saving though methinks =)