You need something that will:
- survive rough treatment
- protect your feet, particularly on site
- keep them reasonably dry in wet weather
- keep them cool in hot climates
- be suitable for use on an archaeological site
- or for walking across rough country (on field survey projects).
Heavy boots with deep treads in their soles mess up the trowelled surfaces on site, but might be what you need for a lot of survey work in rocky terrain.
Walking boots. If you are doing a field survey in open country, you will need proper walking boots. You don't need anything too fancy, but they need to be a proper pair, designed to give you enough support to keep you on your feet all day and with good enough grips on the soles to prevent you slipping. Leather boots are expensive, and there are a lot of cheaper fabric boots now. They are more comfortable and cooler to wear, so they may be a better bet if they will be your main footwear for a long trip. If you are working in a dry climate, then the ordinary fabric ones will be fine. If you are working in wet conditions, you will be much more comfortable with a breathable waterproof lining (Goretex or Sympatex, see below) in fabric boots, and even leather boots. Most walking boots would give you good protection on an archaeological site and, although the aggressive grips on the sole do mess up trowelled surfaces, you do have more control over your feet than with gumboots (below). Whatever you get, they need to be a comfortable fit. When you go to buy them, make sure you have the socks you intend to wear with you and it's a good idea to try them on in the afternoon (your feet swell during the day).
Other boots. You could also go for ordinary work boots on site, although they probably wouldn't be as comfortable. Contractors, riggers and so on have special pull-on work boots with reinforced flat soles, steel toecaps etc. They would be good on an archaeological site too, but I've never tried them.
Lighter walking shoes and sandals. If you are going on a long trip overseas, you might not want to carry heavy boots, and there are now lots of light walking shoes based on trainers. They would probably be fine on a site in dry weather as well - and probably cooler than boots. In addition, the grips on the soles are not quite so "aggressive". Similarly, there is a whole variety of special walking sandals or clog-like shoes. They are popular with people going on expedition type holidays, because they are comfortable, cooler, dry out faster and you don't need socks. Most do support the feet pretty well and quite a few people wear them on site in hot countries. It is debatable whether they protect the feet enough for site work, or field survey, but they make a good second pair of shoes to relax in when you're not working.
Gumboots. In continuously wet and muddy conditions, gumboots will keep you dry and clean. Ordinary gumboots do not, however, offer you much protection from a carelessly swung spade or a sharp nail in a plank. It is possible to buy gumboots specially developed for building sites, with steel toecaps and plates in the soles. These are however expensive, heavy and bulky. Gumboots in general tend to be bulky and therefore pose a problem to anyone trying to carry them in their luggage. The other problem is that the deep treads on a gumboot sole and the heavy clumping walk can rapidly make a big mess of an archaeological site. I know several directors who will not allow them on their site.