I've owned a 96 sport for quite a few years; I built mine with a suspension kit from Kreator with fox coilovers in the front, new A-arms, new control arms and springs in the rear. I'm not 100% certain how many miles are on that kit, but I know over 50k. I bought mine with a blown engine and dropped in an almost-new one several years ago.
The main differences are the lower body panels, frame width, and of course the J18 engine. *most* normal sidekick parts interchange; even some aftermarket parts work fine. Since the frame is wider, bumpers won't fit. A-arms are the same size, but the drop brackets for the front diff are unique to the sport (different than both sidekick and vitara ones). Front brakes are larger; a 15" wheel will not fit which might limit your tire choices. A strut spacer lift would work fine. The Sports all came with 5.12 gears, which is nice for most builds.
I haven't had any problem finding normal parts for the 1.8L; it shares many parts with the 2.0L and 2.3L J engines so it isn't as unique as a person might think. As for OE parts, there are still parts stores carrying Suzuki stuff here in the US but they are diminishing.
The 1.8L engine is a nice step up form either of the 1.6's, but it really doesn't make good power at low RPM's. If you do more high speed high RPM driving, it is a good choice. It's a bit of a pain for slow speed crawling. A relatively easy swap would be a 2.3L out of a 2004+ Aerio.
I would tend to agree with Fordem; if you REALLY want the older body style, the Sport might be a good choice. The newer Vitara/Trackers have come down quite a bit in price and already come with the 2.0 (or 2.5 V-6 in the GV). Your $$ would probably be better spent on one of them if you don't mind the newer body style.
edit: attached a pic of my Sport. It's on 32's in this pic.