While the wristwatch dates back to the early 19th century, it didn't really soar in popularity until the early 20th. Initially, wristwatches were primarily set in bracelets, and worn almost exclusively by women. Men primarily carried pocket watches, and if you look at clothing of the time you often see pockets and accessories designed specifically for said timepieces.

The 20s, in particular, are part of the early period of mass-market wristwatches - and this is due to the influence of military use. In the late 19th century, with the need for coordinated attacks, officers needed to time orders precisely. Pocket watches are more cumbersome in combat, so wrist-mounted ones became preferred. In WWI, service watches were developed and issued for trench warfare, exposing a large number of people to the style. The macho soldier image did a lot to remove the stigma from wrist watches as "feminine jewelry" (indeed, advertisements would specifically reference the wrist watch's place in warfare)

While the pocketwatch is still very prevalent in the 20s, you will definitely see wristwatches on both men & women. Pocket watches are pretty much exclusively male, and pendant/charm watches are female. In terms of price - just like today, you have a range of prices. The cheapest ones appear to be around $1 ($12.45 in 2015 dollars) to some costing $40-$50 (over $600!).

Here's a really interesting article about the wristwatch overtaking the pocket watch - looking at the gender stigma that kept it for so long as a women's accessory, and the factors that led to a huge spur in the mass market.