https://www.dexcom.com/faq/what-devices-and-software-are-compatible-dexcom-cgm-apps
Yes both series 1 and series 3 are supported. However, Apple Watch series 1 can’t be updated past WatchOS 3, this means series 1 can loose support later on, if dexcom update to only WatchOS 4 or higher, not likely but there is always a risk with biting older hardware.
Second, Apple Watch requires an IOS based device to eun dexcom, but I guess you already have an iPhone since you considered Apple Watch, so that won’t be a problem.
So short answer, yes both will work with dexcom, but series 1 are getting old, so I would personally go for series 3 because it is newer, and because series 1 still are «expensive» for being that «old»