i personally don't like the idea of doing things on the cheap. cheap wheels are heavy, and the metal can be soft and prone to buckling/bending. cheap tyres may offer poorer grip, etc. i guess i don't really know how cheap you plan on going, and what compromises you're willing to take (so, no offence
lowering is one thing, but then you'll compromise greatly on ride comfort unless you also upgrade the dampers. i would not drop it more than 40mm without new dampers that can properly control the car (dampen the rebound, especially). at the extreme, worn/poor dampers can lead to a 'bouncy' car, which can badly affect handling and roadholding, which in turn can compromise safety; this is going to be worse on lower/harder springs.
if you wish to retain original dampers, then perhaps don't go lower than 30~35mm. a set of Eibach Pro Kit springs would be ideal for this. nice ride comfort and decent lowering.
for 'lower', consider H&R (if available for your version car). otherwise, you'll need a set of coilovers with adjustable rideheight. but this defeats the purpose of 'cheap'. or else custom wound springs. personally, i'd never go with 'compressed' springs (ie: squash existing springs to be shorter) or 'cut' springs.
stock dampers, and even most normal upgraded dampers, may not cope well with lowering beyond 40mm. they are not operating within their 'sweet spot' of travel (compression/rebound). this could affect performance and also reliability and therefore how long they last. you should consider something like the short-stroke Bilstein B8 dampers which are more specifically designed for shorter springs.
17s and 18s are no trouble, so long as the width, tyres, and offset are appropriate. i had 18x7.5" wheels with 225/40 tyres, and an offset of +35mm (this was on my old 156). only some very minor issues of 'rub' of the tyre against the wheel arch liner at extremes (rear of car heavily loaded with 3 passengers and/or luggage) or full lock on the front wheels whilst driving into a steep driveway. no issues for normal daily driving.
so, determine your priorities. research carefully. and decide what will suit you best. perhaps do it in stages, with some springs, then wheels, then dampers.