What should I be looking for when trying out running shoes? Local store lets me try the shoe and jog up and down the block, but they mostly feel the same to me. Is there some feeling or anything else specific I should be looking for?

If you're starting out, you can get away with daily trainers until you think you need to add more gear into your training.

Some shoes need a break in period to really get to know how the shoe will perform. Some are good right out of the box.

You need to select a shoe that works for you. I don't know your fitness level but a good start is finding a good, durable daily trainer. These work well for low intensity and slow speeds that can withstand distances up to 20 or so km. You could use them for sprint sessions if you want.

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Fit. Heel lock. Bounce. Cushioning. Rebound. Energy return. Responsiveness at different speeds. Support.

A good way to research shoes is to watch YouTube channels that review the shoe. There are several good ones that conduct a thorough review.

Then you got the race day shoes. If you're competitive and wanting to hit a personal best, then getting a super shoe will help with your performance. These are really expensive. They're not made with durability in mind.

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Speed shoes are for that, speed. They usually have some form of carbon plate in the sole. They will feel awful if you're running below a certain pace, but feel great once you surpass that speed threshold.