I'm one of those people whose battle pet has very uneven stats: HP: 501 Strength: 348, Defence: 155, Move: 247, Intelligence: 2808 and Level: 101. I can confirm that due to my pet's insane HP I do have to up my level to 251 before I can train other things (defence). For me the rushing to 250 is a bit more tempting and necessary as I can't do anything else until then.
Whatever you choose to do, keep an eye on those weird little rules and keep your stats fairly even as you go!
Also, look into kitchen quests maybe. They give out stat increases which from memory are fairly decent. Some quests are expensive, but not all so it might be something you think worthwhile.