If you really want to engage in carpentry, it's worth the cost of a thickness planer. Once you have it, you will never regret the expense, because you will be in control of the thickness of your stock like never before. But taking a step back, I agree with Tim. The best tool for thickening material is a dedicated table planer (see photo above).
They don't take up much storage space, even in a small shop, and work great for reducing tables up to about 12 or 13 inches. Width (depending on the planer) up to the thickness you need. Once you have a table planer, I bet you'll never regret the decision; ultimately you won't just pay the prices for pre-planned wood or use just ¾ of an inch. Electric hand planers are like an aggressive belt sander.
They work well on boards that have hollowing and twisting problems. The electric hand planer is not as accurate as traditional manual planers. But they do bring you much closer and faster to where you want to be so that you can give the boards their final touches with a hand plane.