By Swiss standards, it's a problematic neighborhood. In Frankfurt, the same would be middle class. Schwamendingen is ok, as long as you can avoid the airport noise (hint: look at a map of Zurich, draw a line from the runway across Schwamendingen, avoid everything 500m right and left of it). Schools are there, parks and the Zuriberg are close (you can walk to the Zoo), daily shopping is nearby, as are the Glatt shopping centre (best of CH) and IKEA.
first of all, it's Schwamendingen, not Schwarmendingen, that's something else in German.
I work in Schwamendingen, close to tram station 9 Luegisland. I would say that it is not the nicest are in Zurich, it's suburb but it is still ok, and the connection with the city is very fast and efficient. from Schwamendingenplatz, two trams run, 7 and 9. It's definitely cheaper that Zurich center and a good place to start, I think. Also it is close to the airport and the highway.
If the place you have been offered is nice, I would consider it.