Earl J. Hess's book The Rifle Musket in Civil War Combat: Reality and Myth (Kansas) has a chapter on the firearms culture that Civil War soldiers inhabited, and what formed their sensibilities about arms prior to their enlistment. Then, as now, there was an avid interest in firearms and technology, and people followed developments and technological changes quite closely. Thus, many a recruit, particularly in the West (meaning our Midwest and the Southern States bestride the Mississippi) insisted on the best and most modern guns available, even as an enlistment bonus.
What was civilian gun ownership like during the mid 19th century in America?
Commonplace-- Of course historian Bellisles lost his job at Emory for his book on arming America because it was picked to pieces by historians more familiar with its subject, and any number of errors cropped up in the book that were beyond mishandling of sources or sloppy research... An admirably "counterintuitive" thesis, namely, that post-Civil War firearm companies, threatened by insolvency and/or possessed of a surplus of arms, basically "dumped" guns on the postwar public, and created the market demand for their products. Unfortunately, there really was a pre-Civil War gun culture that was heavy into guns.
How much did firearms cost?
Naturally, this varied. A perusal of old advertisements and so on and then looking at 19th century household wealth patterns, wage scales, etc. would show that they were pretty expensive as a rule, and that people viewed them as an important "durable good." To chime in with what people have said up post, many were indeed handed down in wills and estates.
did most people own a firearm, or were they just for the wealthy? How many were heirlooms passed down from generation to generation? Were gun smiths common? If you couldn't afford a gun were there cheaper options?
Yes, no, not entirely, some were, yes, well, there were really cheap gun options. Recall that prior to the United States being a gun culture, it had long been a knife culture... Witness the lore surrounding the "Sand Bar fight" and the elevation of a grifter and mean-when-drunk virtuoso of killing people with a huge knife, James Bowie, into a legend and naming said huge knife after him.
A sword or knife from a blacksmith maybe? Did the variation of gun depend on what region of the country you were in? Were Fowlers the most common firearm amongst the general public
Some of the earliest percussion guns made in the United States were the under-hammers from New England--New Hampshire, Massachusetts, and New York gun makers. A fowler or shotgun would have been almost ubiquitous on farms, which remained for the most part the chief profession. Various regions of the country had become synonymous for particular styles of rifle, and this did not go away overnight.