Switching from 3x9 Gears to Cheaper Ones?
I think you'll find that the cost of switching to a different gear type will be more expensive in the long run.  As technology progresses, the 7 speed stuff will get harder and harder to find, and more expensive.  I've messed around with this sort of thing, but going the other direction: there are a lot of items you'll need to switch.  A short (probably incomplete list):


cassette (obviously)
shifters (obviously)
brake levers (if they're attached to the shifters, as many are)
The freewheel in the rear, to be compatible with the different kind of cassette

May include a new rear hub
May include a new back wheel
May instead include rebuilding the back wheel yourself

Your crankset in the front, if gear ratios are wrong for your new cassette


It ends up being a pretty big change.  That said, you can get 9 speed cassettes pretty inexpensively.  If you're worried about cost, you can get a new cassette for about $20.  You can get a new 9 speed chain for $15 - $20.  If you keep your chain clean, dry it whenever you get it wet, and keep it well lubed, you should be able to get at least 2000 miles out of it.  If you replace your chains when they start to wear out, you should be able to make a cassette last through at least 3 chains.  That's 6000 miles for about $65; not bad.  Considering how much money and time you'd spend on new shifters, hubs, freewheels, and all the rest, I don't think it's ever really worth downgrading equipment.