This might clear some things up, its pretty basic though.
1600's- The main European nations wore fedora-like hats,(sorry, I don't know what they're called, I just have this info in the back of my head, and even searched on Google to check my brain's reliability ) and Morions, (infamously worn by conquistadors) not just the Spanish. People still wore metal helmets in this time period, and in the 1500's, (guns didn't completely dominate the battlefield, because they were still pretty unstable and, well, sucked) and they still had pike-men.
1700's- Tricorns by standard infantry and bicorns by officers. Of course certain countries might have different hats, and and certain parts of the century might be different, not to mention different jobs, special groups, and elite regiments might have different uniforms/ hats.
Early 1800's- Shakos for the grunts, and bicorns for the officers. You've probably seen Napoleon with the bicorn on, or General Washington with one too.
Lots of European nations had varying types of shakos, but if you want to get that specific, get decals and custom hats from the AFOL community.
Mid 1800's- I don't know about the rest of Europe, and all the martial races the British had, but I know for a fact that the American cavalry units had fedoras, the infantry had kepis, and depending on rank/position, the officer can have either one of those. The martial races usually have hats according to their religion/culture(Exp. Sikhs-Turbans). ( You know what martial races are, right? )
Late 1800's- This is about when helmets came back into use, I think a white archeologist helmet would do you good for the British in the Anglo-Zulu war time frame.
Note: Tricorns were also used by the civilian population during the late 1700's/ Early 1800's. Additionally, the helmet used by the British in the late 1800's would work well for a civilian, particularly an archeologist.