Hi Mary. I live in Lörrach, which is just east of Weil, and also work in Basel.
There are a couple of nice areas in Weil that you might consider, but I would avoid the area right on the border (Friedlingen, for example) since that is a light industrial area and a bit rough (at least, rough by local standards). Weil itself is not too bad, but in the end we chose Lörrach. Lörrach has more facilities, is a bit bigger, a bit quieter (which was important for us since we've just had a baby), and IMO nicer in general. Very happy here.
Both Weil and Lörrach have S-Bahn and bus connections to each other and to Basel. Plenty of decent cyclepaths, too.
For finding somewhere to live, a good place to start is the
rentals section of the Badische Zeitung. I think this is where we found our place.
As for a community, there is a large English-speaking community in Basel. See englishforum.ch