Without Hope or Hesitation
The Basics: We will be using 6th Edition Call of Cthulhu rules, which are more or less identical to all editions before 7th. The game opens in New York City in January of 1925. Your character is a friend of the writer Jackson Elias.
CoC chargen relies heavily on random die rolls. Not that I don't trust you, but characters should be rolled up using Byakhee, with the 6th Edition rules pack. Alternately, you can roll up stats using The Keep. Character creation rules (which are simple) can be found in the quick start rules PDF here.
Backup Character: Attrition is notoriously high in CoC games. Characters go insane, get eaten or killed, or otherwise experience things so unsavoury as to be unable to keep investigating. For this reason, after creating your character, roll up a second character. This should be a close friend, relative, or interested party who would be incentivized to carry on your first character's work.
Useful Skills: Everyone says that you don't need to know how to fight in Call of Cthulhu, and I've yet to find a published campaign that doesn't feature pitched battles with knife or gun-toting cultists. At least one combat skill (and dodge!) will likely prove helpful. There will still be many situations where force-on-force will not be an option for the players. Many other skills will be needed.
I've Seen Things: You may opt to have a character be a veteran of one of the many wars that characterized the first part of the 20th century. You may further opt, at a cost of 10 starting Sanity Points, to have seen extensive action; in recompense, you will not suffer sanity loss for mundane things like seeing the dead body of a fellow investigator. World War I was fought from 1914-1918 by Europeans (including Canadians, etc) and the Japanese, and from 1916-1918 by Americans. There were many other "small wars":
Border War (US vs. Mexico, 1910-1919)
American occupation of Nicaraugua (1912)
First Chaco War (US vs. Haiti, 1915)
American occupation of Haiti (1915-ongoing as of 1925)
Second Chaco War (US vs. Haiti, 1918-1920)
Estonian and Latvian Wars of Independence (Britain and a host of small European countries vs the USSR and others, 1918-1920)
Third Anglo-Afghan War (UK vs Afghanistan, 1919; this was a big one and involved poison gas and aerial bombardment)
Allied Intervention in the Russian Civil War (UK, US, France, Japan, and Greece vs USSR, 1918-1920; the Civil War itself ran from 1917-1922)
Polish-Soviet War (Poland with French support vs USSR, 1919-1922)
Irish War of Independence (Ireland vs UK, 1919-1921)
Somaliland Campaign (UK vs the "Mad Mullah" of the Dervish State, 1920)
Great Iraqi Rebellion (UK vs Iraq, 1920)
Irish Civil War (1922-1923)
Adwan Rebellion (Jordan vs UK, 1923)