The simple answer to your question is: use the critters your Taming for gains. A more elaborate answer...
Go to this site:
http://uo.stratics.com/hunters/index.shtml
Click the Advanced Search. At the bottom select Required Taming in the Sort By drop-down and then click Search. You now have a list of critters sorted by Taming difficulty. You need to scroll down to almost the end of that list (Cow) before you get to the Tamable critters. The bottom of the list requires the most skill. The Giant Spider requires 59.1 skill. IMHO the first fun pet is the Frenzied Ostard (77.1) The really fun stuff starts with the Bake Kitsuni (80.7). I love fighting with these guys...they hyena-laugh when they kill something!
If you click on any of the Tamables in that list you will see the critter's spec sheet including the range of stats, resists and skills that a particular pet can have. Obviously a keeper pet should have attributes that are on the high side rather than the low side. Then comes pet training where you try to max-out your pets stats and skills. When your pets skills are low they train fast and easy but at higher levels, they grind. This is why every Tamer, IMHO, should also be a Bard. When your Discord you pet you lower its resists and skills by as much as 28% which makes training much faster and easier. I have a fully trained, lowly Blue Beetle that easily takes on several Earth Els!
Peace and Discord really compliment aTamer template. Discord a dangerous prospective pet and when it hits you it hits for much less damage. Peace a dangerous prospective pet and doesn't hit you at all. When you're hunting, use Peace to control the crowd and Disco to quicken the kill.
You mentioned only your Taming skill...remember in order to control the pet you need both Taming and Lore.
Here's a good site for taming/pet info:
http://www.strangeworld.com/uo/prc/prc.php?Section=training
Here's a handy what-do-I-tame-to-gain calculator:
http://www.tamingarchive.com/main/whattotame.php?skill=98.2