Whether you are swinging a fly in a trout stream or working a rocky surf line for stripers, good wading gear keeps you warm, dry and, most importantly, safe on your feet. It is worth understanding before you buy.
Waders
Breathable stockingfoot waders (worn with separate wading boots) are the most versatile and comfortable choice for most anglers, cool enough for summer with layers underneath for the cold. Neoprene waders are warmer for deep winter but hot otherwise. Stockingfoot with good boots beats built-in bootfoot waders for grip and fit.
Boots and soles, the safety part
Your footing is everything. For the surf and rocky shoreline, studded or spiked boot soles grip slick, weedy rock, this is a safety issue, not a luxury. For trout streams, felt or rubber soles both work (some states restrict felt to prevent spreading invasives, so check local rules). Match the sole to where you fish.
Wear your belt, and respect the water
Always cinch your wading belt, it keeps water out if you go in and can be lifesaving. Wade within your ability, use a wading staff in heavy current, and never wade beyond your comfort in cold or fast water. See the safety notes in reading water and mind cold-water risk.