The best strap for a field watch is almost always canvas, nylon, or leather in an olive, brown, or black tone, since these materials match the rugged, no-fuss purpose of a field watch in the first place. The right strap should disappear into the watch's overall look rather than compete with it.
Why canvas and nylon are the default choice
Field watches were designed for rough conditions, and canvas or nylon straps hold up to that better than almost anything else. They dry quickly if they get wet, they do not crack the way cheap leather can, and they age into a worn-in look that actually suits the watch instead of looking beat up. A NATO-style strap in particular is a smart pick because it loops under the case and through both spring bars, so even if one spring bar fails, the watch stays on your wrist instead of falling off.
These straps are also inexpensive enough that owning two or three in different colors makes sense, letting you switch the whole look of the watch for a few dollars instead of buying a new piece.
Where leather still makes sense
A quality leather strap works on a field watch too, especially if you wear it more with everyday casual clothes than in genuinely rugged conditions. Look for a leather that is treated to resist water and sweat rather than a dressy, thin leather meant for suits, since a delicate strap will not last on a watch meant for outdoor use. Distressed or oiled leathers in particular tend to hide wear well and only look better with age.
Whichever material you pick, stick to widths and colors that match the watch's original design intent. A too-shiny or too-formal strap on a field watch usually looks off, no matter how nice the strap is on its own.