The method that comes in the booklet will easily get you under a minute. My best time with it before learning a more advanced one was 34 seconds, so you can most definitely get under a minute with practice.
With the times you're at now, it's just practice that will help. You could learn a more advanced method, but it's not your method holding you back right now; it's inexperience. You need to practice looking ahead at the pieces you will be solving next, you need to practice your turning speed, you need to practice your algorithms until they're fast and mindless.
Once you get down below a minute, you'll start being ready for a new method. Fridrich is probably the easiest to pick up, but Petrus and Roux are both good alternatives if you don't mind a bit of re-learning how you approach the cube. There's other methods too, but I'd recommend one of the big three before tackling ZZ or Heise, for example.
The lower your times get with your beginners method before switching, the faster you'll pick up a new method. So, it's really a matter of preference. If you feel you understand enough about the cube to get more advanced, then do it. I'd wait until at least sub-1 minute though.
(under a minute to solve) Thanks!
