Yup, clipless is the way to go. You should be making contact with the ball of your foot. You will have stiff road shoes which will enable you to push with your entire foot. That is important because pushing with different parts of your foot engage difference muscles - e.g. - pushing with your heels engages the glute muscles & makes it easier to go uphill.

Another bonus is that you can pull back (engaging the hamstrings) and thus be pedaling in a circle. You can avoid mashing the pedals, overusing your quads and possibly inviting knee problems.

I really recommend moving to this as soon as possible so that you will teach your legs muscles how to properly pedal a bike. Muscle memory is a powerful thing and you don't want to be a masher!