This was me 2 years ago. Masters workouts were more (way more, usually) than I could do but it was a pleasant enough experience. Not Arlington, though.
Here's a place to start, both for a workout plan and just getting familiar with some of the terminology:
http://ruthkazez.com/swimming/ZeroTo1mile.html
With a solid fitness base from running, I can work up to the mile pretty quickly with just one or two swims per week. (As in, number of weeks to do it ... it's still a slow mile.) I start with her week 2 or 3 workout and just increase from there.
I only swam with a masters team for one season but I wouldn't hesitate to do it again if I wanted more swimming or serious improvement. I would probably start with the routine above and try to get some of that early awkward swimming out of the way before going to a group session, but that's mostly because you'll get a lot more out of the session that way.