A wheel consists of a hub, a rim, and spokes. On the hub, one puts either a freewheel or a cassette, depending on the type of hub. (low-end or old fashion hubs use freewheels, modern hubs take cassettes.)
Your spokes are toast and your rim is probably of inferior quality, so you basically have 2 options:
-Buying a new rim, new spokes and have a new wheel laced around your current hub. I would not recommend this option, since your bike shop doesn't seem to have great expertise on building and tensioning wheels, and buying all parts separately + labour is generally more expensive, especially when buying low to mid-end stuff.
-Buying an entire new wheel. This is probably the best option. This new wheel will have a modern (8/9/10 speed compatible) cassette style freehub, but it's perfectly possible to put a 7-speed (the number of sprockets of your cassette should match the gear shifters and derailleur of the bike) cassette on that hub.
If you're worried that you're putting too much stress on the wheel from accelerating too fast in too high a gear, then the obvious solution is to accelerate slower and in a lower gear. Wanting to fix a problem by throwing a bunch of money at it, when you yourself believe you could fix it by a free change in behavior but choose not to, is what is complainypants.Of course, that assumes that you're correct in thinking that the torque is causing the spoke breakage, which DagobertDuck disputes. If he's right, keep riding however you want.
I am right. Accelerating hard (high gear, low gear, whatever) doesn't cause spoke breakage. Too high load (luggage or body weight), too low spoke count, too light/weak rims, and above al: inferior build quality do.
The wheelset I have on my roadbike, built by a very good wheel builder, is still going strong after 40.000 miles, never broke a spoke, not even needed any trueing.
He's telling you that if you want to buy a new replacement wheel then you can just get an easy-to-find 9-speed one, remove the 9-speed cassette, then put on a 7-speed cassette (and spacer) so that it works properly with your existing derailleur and shift levers.
Wheels usually come without a cassette ;)