It depends on the starting control slot of the pet and how you go about training it. Slot really doesn't matter.
Here are the key facts:
- Every time you train a pet, you increase the control difficulty by 2.4. It doesn't matter if you gave it 1 str or 500 str. Everytime you "apply" any stat/skill change to the pet, the control difficulty goes up by 2.4.
- Every time a pet increases in control slots, the control difficulty will increase by 21.2 (it's actually 18.8, but the 2.4 from training it is lumped into that number because you have to apply training to get it to increase in control slots)
- The Vollem levels slow because it starts with a negative control difficulty, giving you lots to work with
So if you want to maximize your pet for a certain control chance, you need to carefully plan out your spec and "apply" training as little as possible.
However, as was mentioned above, it will be fairly difficult to make a pet that remains low control difficulty unless you make sacrifices. Giving your pet resists, str, dex, stam, and base damage would increase its base control difficulty by 40.4 with just adding those alone.
Edit:
If you want to know what Taming/Lore you will need for various control difficulty, see my post here which provides the control chance formula:
Beetle Control Chance