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>1. ) Boot or shoe
Boots are generally better for hiking with heavy gear, in wet terrain, snake country, or cold weather. They are also cheaper cause they last longer.
Shoes are lighter and softer, which fatigues you less, but offer less protection.
>2.) Price
Don't spend less than $100 or more than $200 (shoes) or $300 (boots). Within that range, price is a secondary concern. If you get the pair which fits just a little less perfectly but costs half as much, you'll end up buying the more expensive pair later after your first hike.
>3.) Fit
Most important consideration. You should be able to fit one finger behind your heel if you scoot all the way forward inside the shoe. Your heel shouldn't lose contact with the sole while walking. You shouldn't feel any pressure points anywhere on your foot, but your foot shouldn't slide around inside the shoe either. Try on as many pairs as possible and compare. If buying online, don't fixate on one model, find 5 that you like, google them to find out if they have a narrow or wide fit, order 2-3 and send all but the best pair back.
4.) Materials
Gore-Tex is better than leather in cold and wet climates initially, but the membrane will be the first thing to give in, so after a year your boot will be LESS waterproof and breathable than an all-leather boot.
All-leather boots are a better long-term investment IMO, they need breaking in and more maintenance, but if they're well waxed, they're virtually water proof, can be resoled and there's no reason you shouldn't still have the same pair after 10 years+ of use.