Footwear is really important for walking in the mountains. It helps you move around as efficiently as possible.
A good pair of walking boots should hold your foot in a comfortable position, give you angle support for going over rough terrain and give you grip on different surfaces.
There are a few different categories of boot that are suited to different conditions. These categories are often referred to by manufacturers as seasons.
A 1-2 season boot is best suited for light summer walking on decent paths. They are a much softer boot with less ankle support for rough terrain and often not particularly waterproof. They are easy to put on and usually fairly comfortable out of the box. I would recommend these boots if you are only planning on doing easy paths in the summer.
3 season boots are more of an all round boot for the mountain and what I would recommend for most walkers. They offer much more ankle support for keeping you stable on rocky terrain. They also have a stiffer sole giving you a better platform to stand on in soft ground and have a more aggressive tread pattern for more grip.
4 season boots are more for winter use. They are much thicker to keep your feet warm, have a stiff sole that allows the attachment of some crampons and hold your ankle in place. They are often to0 warm for summer use and feel more clunky and heavy for general walking.
It is hard to find a good boot that fits you well but searching for one that fits you will make walking a lot more enjoyable. Most brands have slightly different foot templates and therefore there is often a brand that will fit your feet better than others.
Rather than suggesting certain brands or features, I suggest you go to a shop and try on as many different pairs of boots as you can to find what ones fit your feet best. Take your time, let your feet settle into the boots, have a walk around and see what boot is best for You.
Also, think about what you need your boots for. For instance, if I was planning on going scrambling up a ridge in the summer then I would want a light boot with plenty of grip that lets me move my ankle around slightly for climbing over rocks. If I was going on a multi-day expedition travelling a long distance then I would want a warm, well supportive boot that keep me going mile after mile.
As always, if you have any questions, please ask below.