To Clip or Unclip
Just like on a road bike or a mountain bike, going clip-less, (which actually means you clip into a pedal mechanism with a cleated shoe rather than using toe clips with an athletic shoe) gives you the most out of each pedal stroke.
When you go clip-less you can actually pedal in circles. In other words, you will use all of the muscles involved in pedaling. From the top of the stroke, going forward and down until you hit the bottom of the stroke, you will be using one set of leg muscles. Then on the back upstroke, you will be using a complementary set of muscles. By pedaling in circles, you will keep your leg muscles in balance and get more power out of each stroke. If you ride on the street or on trails this extra dimension of pedaling in circles will give you better control of your bike and will also get you better results for the amount of energy you are expending. You will go faster and further.
The Shoe, the Cleat, the Cost
So you've probably figured out by now--if you don't have cycling shoes--that to go clip-less, you will need above said shoe and cleats that match the type of pedal that is used in your gym. Most gyms use SPD style pedals that are compatible with SPD style cycling shoes, which in turn use SPD cleats. So how do you know if a cycling shoe is SPD style. Easy. On the bottom of the shoe you will see two parallel slots, with screw receptacles in each slot. The SPD cleat matches up with these slots. This type of setup is also used for mountain biking (as opposed to a road shoe set up which uses a totally different type of cleat). You will need to spend some money to buy the shoes and the cleats, but once you do, the shoes should last you years if you only use them in the gym. I suggest you get a recreational type of spinning class shoe or a recreational type mountain bike shoe. Both will be flexible and comfortable and won't break your bank. The mountain bike shoe will be a bit heavier, but you might also use it for your lighter duty mountain bike rides, if that's your thing. Expect to spend from $70 to $125.