The "new cable stretching" thing mainly happens for the first 5-10 hours of riding.. they'd be settled in after a couple of weeks.
Assuming you have the L and H settings right on the rear derailleur, it's a fairly simple procedure for adjusting cable tension.
If you have trouble shifting to a slower gear -- cable doesn't have enough tension to move the derailleur cage to the right spot -- turn the little barrel adjuster on the rear derailleur COUNTER-CLOCKWISE a bit
And vice versa, if you have trouble shifting to a faster gear, there's too much tension; turn the barrel clockwise a little.
Only do about half-turns at a time until you can get it dialed in. Actually there's another barrel adjuster at the rear shifter unit too, but the one at the rear derailleur is usually easier to use because there aren't a zillion cables around the place.
For the front derailleur the L and H screws control where the derailleur is for the granny and big rings respectively; the cable tension adjustment will influence where the derailleur sits for the middle ring. There's usually a barrel adjuster on the shifter unit for the front. As for the rear, counter-clockwise turns increase tension, clockwise decreases it.
If no tension adjustment seems to work right, I'd then look at replacing your cable inners and outers. (From experience, replacing inners but not the outers works sort of ok, but not for very long..)
In any case cable inners & outers are cheap, especially compared to the cost (and time cost) of hunting down 7 speed shifters etc. 9 speed LX (as on your bike) is definitely not junk and unless it's been damaged, will be able to be tuned to perfection and should keep it.