Switching from 3x9 Gears to Cheaper Ones? Alert I am unsure of the right terminology for gear-wheel but I mean the round things near pedals such as 3x9 or typically with 3x7 (3 front, 7 back) mix in commuting bikes.

My current gears are 3x9 (3 front, 9 back) but I plan to change to cheaper, the current gear-wheels are used (about 15k km, 4winters and 3 summer). 


Can I put other gears such as 1x7 or somehow reuse the old gears? 
What should I take into account when choosing other gear-wheels and gears? 


There is nothing problem with my current ones, they work fine (a bit slower than as new but not a problem) but I cannot spend too much on upgrading the gears/gear-wheels. I need to know what to look for in second-hand stores or to find some sort of compromise i.e. perhaps to upgrade things slowly part-by-part.
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.