Same car as mine, the bargain basement baby Bimmer!

Welcome to the 'club!
The sedan is a great car, even better than the coupe IMHO. I use it to tote my family around, two more doors are oh-so-helpful in my situation. Given that my A/C is defunct, those rear windows substantially assist with ventilation. The sedan's resale value is pretty low too, so you don't have to worry about selling it off if you change your mind. Otherwise the two cars are pretty much identical. An iS shouldn't get modded - but the sedan is a whole different creature. Your options are definitely open. I've been upgrading mine for maximum fuel mileage. Is that a sleeper?

I'm averaging nearly 30MPG with a few mods.
IIRC, unless you want to run spacers, the iX wheels will need spacers and longer log bolts or a stud upgrade. They also tend to be expensive - not sure why. Too rare from iX off-road hijinks?

I use
an online calculator to check my math. IIRC, stock 14x5.5" steelies are a 35mm offset; 15x7" iX rims are 41. That gives the iX rims 25mm less backspace, about an inch. That's a bit tight for the strut, but a 25mm spacer could help out. You'd have a lot more rim under the fender too, it'd probably look great. I'd grab the iX cladding too, always liked the way that looked on the boxy little E30 sedan.That iX is totally different from every other E30s in many ways - AWD system, aluminum front subframe, shorter struts, odd cap bearings, etc. Given the number of cars that run the 4x100 hub pattern with a 68mm hub, you should be able to find a really decent & cheap aftermarket rim with a perfect offset for about the same money. Plus, you know they'll be round!
I run stock 14x6" bottlecaps on my E30 (et35?), though the 14x6.5" basketweaves were a nice upgrade. Keep in mind that bigger circumference rims will also lower your effective diff ratio - and the car will be even slower! You could use low-profile tires, but then that famous BMW ride quality takes a beating.
Another (admittedly expensive, but good) solution is a 5-lug upgrade. That'd open you up to a lot of different wheels, and some nice brake upgrades. If you luck out, you'd find an E30 M3 setup. If not, use offset E30 M3 bushings with late E36 control arms/knuckles/brakes/E30 ball joints, GC coil-overs with shorter Bilstein struts (the iX or VW Corrado Billy Sport strut is a good choice). On the rear, grab a six-cyl Z3 rear end. Seems like a straightforward swap. After you've done all that work, you'd need larger rims with less offset, like 20mm or so. The E34 and E38 ran a lot of good looking low-offset rims, and they're pretty cheap.
Euro 15x7.5" BBS basketweaves or Alpina rims do show up from time to time, but they're spendy. I have a set of cheap ASA 17" rims on my 745i, they're surprisingly high quality.