Couple of other points to consider -
If you have to use the stick frequently, you're using it incorrectly. Two mistakes I commonly see: first, if you put your 'ask' on a ten point scale, the first ask should be a 1, the second a 4 - 5 and the third should be an 11. Most people start at 4, go to 5, then to 6. This teaches the horse to wait for the 6 or 7 ask. There needs to be a big difference in the size of each ask to give the horse the incentive to listen for the first, little ask.
The stick behind your leg, in this schooling scenario, is saying "HEY!!!!!!!!!YOU!!!!! I just gave a leg aid and you weren't listening!!!!!!!!!" What most people have the stick say is "Ummm, Excuse me? Are you there? Would you mind listening to my leg now, okay??"
The mistake is nagging the horse with the stick, and then settling for a half hearted or mediocre response.
You've used the stick correctly in this schooling scenario when the horse shoots across the arena in surprise. The other poster who mentioned holding the mane so you don't inadvertantly grab at the horse's mouth when this happens was spot on. Praising the horse effusively for the forward motion, whatever it was, is critically important as well.
To the OP, when you're beginning this process, it's a great idea to have an instructor or knowledgable friend on the ground to help and keep you honest. We all make excuses for our horses, more excuses for the ones we're fond of. Someone on the ground who can gauge the size of the ask and give you feedback is very helpful.
Better still would be an experienced rider or instructor to do a little 15 minute school of your lazy boy first, then have you get on, but I understand that may not be an option for you.