I’m a big fan of snap starts in general, but they take some practice and are a little tricky with responsive. I hold the string somewhat taught with my NTH and snap with my TH trying to get it to pop straight up in the air while I release the string in my NTH.
I’m not a fan of the stomp or tossing it, but if you’ve got a responsive you can try the one where you raise your TH over your head and hold the yoyo directly in front of you with your NHT and let it pop off of your thumb to give it spin. This is in the yotricks video below.
There is also something like the engineer’s windup (kind of like the first in this video).
It sounds like, whatever method you’re going to choose, you need to work on getting it spinning. The engineer’s windup is pretty straightforward since it uses the string to wind itself.
If you want to learn snap starts, I recommend practicing while doing something else, like watching TV, by holding the string about 6 inches above the yoyo with your NTH and just practice snapping to get it to spin with your TH. This way you can just practice the motion over and over until you can get enough spin consistently to try to bind it.