Indiana_Jones_1987: Most firearms available in FO4 and FO76 were, in my opinion, brilliantly done. As a fanatic of archaic firearms of the early 1900's, I was amazed by those double-barrel shotguns and the wonderful Thompson 45. Are these types of armaments available in New Vegas?
The game has a wide variety of weapons. If you don't mind some spoilers check this table: [url=https://fallout.fandom.com/wiki/Fallout:_New_Vegas_weapons]https://fallout.fandom.com/wiki/Fallout:_New_Vegas_weapons[/url]. In overall some of the weapons resemble those in F4 and F76 and some remind of F1 and F2.
Indiana_Jones_1987: Should I play Fallout 3 before New Vegas? If I do not, will I miss any of the story essential to the enjoyment of Obsidian's game?
You won't miss much by not playing F3. New Vegas more frequently refers to F1 and F2 rather than F3. So it's more suggested to play the first two games than the third one.
Indiana_Jones_1987: And finally, is weapon customization an option?
Yes, you can mod weapons in NV.
In general you won't be disappointed. NV is a great game if only you don't mind aged graphics and whiling to risk some potential crashes. :)