Cool find for $20. An alloy wheelset from another cheap/donor bike would probably be the cheapest route. I'm not sure how long the reach is on the stock brakes, but if you were going to buy a brand new wheelset I might look into a 700c set that you could take with you to another frame eventually. It looks like the Berkeley that year was 5 speed so the rear spacing is probably 120mm. You could squeeze in a 126mm 5 or 6 speed wheelset but the 130mm wheelset linked to above would probably require spreading the frame.

Steel wheels are definitely heavy but they could work fine on the bike depending on what you are planning on using it for. It might be cool as a neighborhood / townie bike / grocery getter if you put some upright townie bars on it with one of the wald front baskets since they're supposed to be really easy to mount with a bolt-on front wheel.