VEX and Lego (NXT/Mindstorms) are good choices; one that is often overlooked is fischertechnik.
However, none of these are particularly "economically effective" for a classroom/lab environment with more than a few students, unless you have a large budget available...
Not sure what you mean here; building robots from junk, or from purchased parts (ie, machining/drilling metal/plastic to make the mechanical components; soldering up a PCB for sensing and/or control aspects, etc) - is pretty much the epitome of the "scratch approach"...
If you mean "kit approach", then the aformentioned systems of Lego, VEX, and fischertechnik, among others - are the direction to go; just don't expect them to be cheap (because they aren't).
One other approach (though it can be just as expensive as the kits, and may not be applicable to an educational environment) would be to use off-the-shelf metal extrusions (particularly alluminum t-slot extrusions) for building the chassis (simple hacksawing and bolt-together design). Another possibility is looking into "gridbeam" construction for a robot chassis (you can make your own wood gridbeam, or find someone to make it for you, or you can use steel/alluminum gridbeam if you want something stronger). You can also mix and match parts from the kits (purchasing them separately), along with other off-the-shelf components, and junk/thrift finds...
I have access to a machine shop, and I do my own dbl sided PCBs and MCU systems. So I hope for overall guidance . I want to learn to create bots etc from scratch not from kits in the long run.
G'day Mosaic,
lookup line following bots for a starter then you can get kids to lay tape down in any configuration and then the bot can follow the tape. Better still make it a solar powered bot so if it does run out of energy it will stop then after a short time continue on it's own accord. If the kids are really interested make a few exactly the same then make the same course of each bot and run a book on them. Ya never know even grownup with a few ales under the belt might even come around and place bets.