If you are hiking, you are using your feet. It is important to choose appropriate and comfortable footwear. The type of shoe you wear depends on where you are going and the terrain you will be crossing, as well as what kind of pack you will be carrying.
For most day hikes, a light hiking shoe or even running shoe will be just fine. Many shoe brands offer trail running shoes that have a bit more tread and a more structured upper, these are a great hiking choice. A light, low-cut hiking shoe is the next step up, being constructed a little more sturdily than your typical road/trail running shoe. A full hiking boot is what you look to for rocky terrain, going off trail, or when you are carrying a heavy pack: these shoes offer the most support for your foot and ankle, helping you to stay safe.
Whatever shoe you wear, try not to take it on a super long hike the first time you wear it: you may need some breaking in time to avoid blisters, and definitely don’t want to realize the fit is too small when you’re already 8 miles down the trail. Speaking of sizing, remember that your feet will swell slightly during activity, so be sure you feel a bit roomy when you slip it on at home or in the store. Not too roomy, of course, a sloppy fit is guaranteed to give you blackened toenails and heel blisters!
Socks are the important transition from tender foot skin to boot. Try to find socks that are taller than your shoe to avoid getting dirt and pebbles in between your foot and sock. Try to find wool or synthetic blend socks. These materials help wick moisture away from your foot, preventing blisters. Many brands also sell hiking-specific socks, which have careful shaping, arch support, and are sized for your shoe size. Find ones that fit, fall in love with them, and you will never go back to the non-hiking shoe, I promise!
Personal note: I tend to hike in my running shoes 80% of the time. I find that I know the shoes, I have broken them in, and I generally pair them with a pair of thin wool hiking or running socks. I tend to get blisters on my heels, where I have a bony heel spur, so I pay special attention to how my shoes heel is shaped, and often put a preventative padded ‘donut’ (first aid kit!) around the spur to cushion it from rubbing.