Welcome to Arlington. Perhaps the best thing to do is to download the Bike Arlington map. It shows Arlington and a good bit of “downtown” DC.
I ride from Ballston to Union Station quite frequently, and it’s a pretty low stress route. Mixture of trails and quiet(er) streets. I prefer the wide sidewalks on Memorial Bridge over the narrow TR Bridge.
In the mornings, it’s usually pretty calm to ride Jefferson along the mall (hence Memorial Bridge being a good option). Afternoons on Madison coming back, however….