To tame pets you need to be at or above the minimum taming skill. However, at minimum taming level you'll either get very lucky or spend ages trying to successfully tame it
I'd suggest boosting up as high as you can with skill items when you go out taming to speed things up as much as possible. I found 110-115 was great most of the time, so you don't need to panic about a 120 scroll just to tame new pets.
One of the best pets for a new tamer is the bake kitsune. You can have 2 plus an ethy or other 1 slot mount and you'll easily have 99% control at GM/GM. I'd recommend them as they'll give you the practice handling multiple pets while being mounted. And they giggle
Nightmares, normal dragons and rune beetles will be under control at GM/GM so you're fine for those already. Cu sidhe are a bit harder to tame/control so you'll either need to train a bit or use skill items to get going with those.
I tend to add 5.0 skill to the minimum taming level of a pet to figure out when I should be able to control it about 99% of the time. That's not a particularly scientific way of looking at it, but it gives you a quick ballpark figure when you look over the taming difficulty figures.
Just to clarify, you don't have to have 99% control, but I think when you're new to taming it's good to avoid concerns about pets ignoring commands. So I would suggest you try to aim for 99% control if you can, and keep an eye on their happiness with regular loring, especially if your control % is lower. Keep a stash of food in your pack to boost happiness up and you're good to go.
Wenchy