No one has taken a shot at your question yet - so although no expert I'll take a stab. Those who study this stuff may wish to weigh in if I err.
You don't specify what the boot is intended for, and I will presume you mean a boot as we have come to understand it for the period, not a brogan or other type of lace up boot. So the question is would this be for a farmer/workman or cowboy. By the era you describe cowboy's had somewhat of a boot that was unique and referred to as such. If it is the former then you would be still looking at a common boot not unlike the military had worn from before the civil war, they changed little. A low heel stove pipe type boot of 10 to 14 inches - maybe taller, particularly if you are trying to look cool in the 21st century at an event. Such boots are available from Missouri Boot and Shoe for a reasonable price. And as discussed elsewhere recently they have an excellent product.
If you are talking about a cowboy boot, it evolved from the 1870's on thru current times. A good overview with lots of pictures can be found in the coffee table book "Cowboys: The Trappings of the Old West" by Mann and Flood. Well worth the money if you are into the cowboy stuff. A more detailed discussion can be found in the "Cowboy at Work" by Ward. That book is an absolute necessity if you into cowboying at the turn of the century, tons of great info.
Looking thru those sources, by the 1880's there was a distinct boot type called a cowboy boot that was very desirable - see Teddy Blue Abbot's comments in his book. Sometime during the 1880's you began to see more boots with the separate front bottom quarter and what I'd call a tongue extending upward - not unlike modern cowboy boots. The boots became more decorative, with stitching in the tops. Height could vary. Square toed boots were common, but you begin to see more round toe boots - American cowboys wearing pointy toe stuff doesn't show up until well into the 20th century.
One maker of period looking cowboy boots that I have heard good things about is Brian Allison. His stuff looks good on his webiste, my only beef is I think he pegs his soles and I believe that by the era you describe most soles were sewn. But that may be a small point.
http://www.snowcreekboots.com/Absolutely correct looking boots, in my opinion, for the era prior to 1875 are best served by custom boot makers. But for a cowboy boot from say 1885 on you may be satisfied with off the shelf suppliers if you select carefully. First, find an image of a boot you like with a known date - the sources above are good - and then try and match it to what you see. The soles should be all leather. Hopefully you can live with the fact that these 20th century boots have the heel set ahead of the side seam, to be set at or behind the side seam was a mark of period makers. Also some boots of the 1890's and the silent movie era that you may admire tended to have very under slung heels, something that is hard to find by a period correct maker. These under slung heels are somewhat similar to modern buckaroo boots. If you find boots with the underslung heel make sure you don't get a pair with that stupid, useless "spur shelf". There are some off the shelf boots that claim to be authentic that have that feature, all is not lost, if you like the boot take it to a shoe repair guy, and have him grind that sucker off keeping the general contour of the heel.
Below is a pair of off the shelf boots I got, with leather soles they really work well for my 1890 cowboy persona. Probably less than $150. They have been used for over a decade in cowboy mounted shooting and as you see have held up well. Ignore the horsehead spurs, they are turn of the century, but put a set of OK spurs or period north and judds on them and no one is going to say you are less than authentic.
Hope that helps.
Amended: Woops, blame photobucket for that one, I don't know what happened but you get the idea.