I am not into the social side of things, so I will talk mostly about the instruments.

The square and the grand were the most commonly manufactured types of pianos in the US until the latter part of the 19th century. It is until the 1870s that upright pianos really start to take off (this change happened in Europe around 10-20 years before). Those 1870s uprights would be 120+ cm tall (they were actually measured in inches, so 48" and taller), and quite heavy (squares aren't exactly light, by any standards).

Square pianos were the most common for domestic use, because they were cheaper and smaller. We still have some uprights from the 1860s, some are restored and some are in atrocious conditions. Squares are becoming less easy to find these days, they were problematic back then (from an engineering point of view: HORRIBLE designs) and nobody wants to have anything to do with them these days, but there are some still around. Squares are rescued these days because of their lovely cases, most found in the wild are not very playable. The squares that are restored are not particularly great instruments to play (seriously horrible designs, it's a pain in the ass to work on them).

So, the options back then were grand piano, square piano, and you were finding more and more uprights. Here's Schomacker & Co.'s catalog from 1875, and here's Chickerin's from 1880. I couldn't find catalogs from the 1860s, but these will give you a good idea what was out there (just keep in mind there were probably less uprights).

From the pianists perspective, the grands were (and still are) the best instruments. Squares were inferior (weird action, not the best sound), but cheaper (that's what you would find in most homes with a piano). Uprights were better than squares and cheaper than grands.

What about player pianos (self-playing pianos; pianola is a brand of those)? Those were not around in the 1860s, the earliest functional one would be from 1876. These instruments started to become popular in the 1880s, and they heyday lasted from the turn of the century to the Depression.

Piano makers in the US were at first located in the East, and by the 1830s-1840s we find people making them in the Midwest. So, by the 1860s your piano would have to make some traveling to arrive to the West. Was is strange to buy a piano from far away? Probably not, piano makers printed catalogs and instructions were included to order your piano, and it's not rare to see mentions of sending pianos to costumers in many cities. There are some materials printed by piano makers in which they give instructions about how to unpack the new piano once it arrived to its final destination, and it all sounds like they probably was no knowledgeable piano store people around to help you. These printed materials also mention it's important to get a knowledgeable tuner/technician, and warn of quacks.

I have no idea about the state of the pianos in the Old West, but I suspect they were not very well maintained.

Pianos are rather simple machines, but they have many moving parts. They were (and pretty much still are) made of metal, wood and wool. They need to be tuned regularly, and the mechanism has to be regulated once in a while. However, you can make do and deal with an out of tune piano with a badly adjusted action. It is not that difficult to get the damn thing to have all keys working, but it is difficult to have a piano in great working condition. I assume the warnings of pseudo tuner quacks were there for a reason, but I guess people managed without professional help.

Out of tune pianos have a particular sound. They sound kind of bright and obviously uneven, melodies and clean harmonies don't work well in those situations. However, rhythmic music will work much better, and the extra brightness might work well in not so quiet environments... As long as most of the keys are working, a piano could be used.

additional question: did the average 1860's saloon have a piano, or is that a hollywood thing?