What was the every day carry gear of the earliest British and European immigrants to North America? That's a very good and interesting question indeed! I have not read deeply on this subject, but I have the vague impression that nearly all of them were literally "babes in the woods" and very nearly clueless about what they would need to survive in this new land or even how to use the items they needed. Without some helpful and hospitable Indians we might very well not be on this continent today.
I think we would all like to presume the early colonists had at least enough sense to know they needed a knife of some kind, possibly a hatchet, too, and a flint and steel with some char cloth to go with it. Perhaps many of the grown men carried and smoked a pipe and tobacco or some substitute for it. (All sorts of things were smoked.) The pipes were no doubt lit using twigs from a fire, not by using the flint and steel itself. In the actual settlements themselves some men might have had a small purse for a few coins, though their money might well have been next to worthless at first in this wild land. If a man ventured beyond the borders of his settlement I can easily see that he might have carried a pouch with some jerky, pemmican, or dried fruit or berries in it, a cloak and a bedroll of some sort, and, of course, a flintlock musket, possibly a matching pistol, a long knife, and the powder, balls, patches, some form of grease, spare flints, vent hole pick, and the other necessities to keep his firearms operational. A crudely forged spoon and fork may well have been part of a man's gear, and a drinking cup or dipper, often carved from the burl of a tree (and called a noggin I believe), would have hung from his belt or sash. Not too long after the arrival of the colonists, the trappers, traders, and long hunters developed what we know as the possibles bag slung over a shoulder to carry most of their small miscellaneous gear, often with a bedroll strapped or tied below it.
Maybe I'm all wet on a few of these details, but I don't think I'm too far off.
Some excellent books to read concerning the early times in America are those written and heavily illustrated with wonderfully detailed drawings by a fellow named Eric Sloane. I don't remember any that go quite as far back as the earliest colonists, but they will give you a better feel for the period than anything else I've run across. I think Eric Sloane's books are out of print now, but they can still be found on Amazon and other sources. A good one to start with is "Diary of an Early American Boy." If you want to know more about the tools, materials, and methods of our ancestors I urge you to read what Eric Sloane wrote.