I don't proclaim to be an expert, but I'm more than happy to share my experiences:
I've had 16", 17", 18", and 19" wheels on my 9-3s. 16 inch for snow/winter. 17 inch stock size, but looks a bit small for the larger wheel wells/body lines of the 2008+ cars. 17 inch was perfect for 2003-2007 cars in my opinion. 18 inch is perfect for 2008+ cars, like Diggs said. 19 inch looks great (some will think it's too big) but ride quality will suffer and tires are more expensive since you're dipping into the 35 series rubber.
It also depends on where you live and what the road quality is like in your area. If, say, you live in Arizona where the roads are near perfect, I'd have no reservations running 19s. If you live in NYC or Detroit, I'd be running 17s. Not to say that everybody should do those things, and of course to each his own.
I would avoid running hub adapters as they are at least 1 inch thick, which might do weird things to your wheel/suspension geometry. Plenty of 5x110 options nowadays (not so much back in 2003 when the 9-3 launched!) since other brands are adopting that bolt pattern (Fiat, Chrysler, Dodge, Jeep, Alfa Romeo, and some GM cars). Plenty of people have run hub adapters or wobble bolts without any issue - I just prefer being able to bolt directly and properly to the vehicle hub.
If your goal is deep concave wheels, the only way to achieve that is going with a very wide wheel (usually at least 9-9.5" wide). A few people here have done just that, but spacers are required to keep the tire from rubbing against the strut and shock.
I'm currently running 18x8.5 wheels with 245/40 tires, stock Aero suspension on my '08. The 18 inch wheel paired with the beefy 245 tire is great for everyday driving on our crappy Midwest roads. The sidewall is essentially flush with the wheel with just a tad bit of tire protecting the wheel lip.
On my 2009 2.0T, I had 18x8 wheels on 235/40 rubber which was a similar driving experience, here is a pic - car is lowered on Eibach/Koni Yellow:
The same wheel on our 2008 SportCombi, stock suspension:
Here is a 19x8.5 wheel with 245/35 rubber on my 2009, Eibach/Koni:
Finally, here are multiple angles of a 19x8.5 wheel with 235/35 rubber on my '08 Aero with very low KW V1 coilovers. Very impractical and annoying to daily drive. 19 inch wheels look weird on our cars unless you are also significantly lowered, in my opinion.
I bought my current wheels from a UK seller on eBay. They are incredibly high quality wheels for the price, I'm very happy with them. These are what I bought:
https://www.ebay.com/itm/ALLOY-WHEE...-FOR-SAAB-9-3-9-5-93-95-9-3X-900/173904781190
Take a look at all of his offerings in the 5x110 bolt pattern, plenty of tasteful choices in both 18 and 19 inch:
https://www.ebay.com/str/jjt-auto/5X110-ALLOY-WHEELS-/_i.html?_storecat=2959200016&_sop=15&rt=nc
Really can't beat those prices, free shipping from the UK for 100 pounds of wheels is insane. These are not cheap knockoffs either, the finish was flawless and they balanced without issue.
Doing a search for 5x110 18 on eBay nets about 8,000 results. Take a gander:
https://www.ebay.com/sch/i.html?_fr...110+wheels.TRS0&_nkw=5x110+wheels+18&_sacat=0
Change the 18 to a 19 if you want to go that route, same idea.
TireRack and DiscountTire 5x110 options are limited and all ugly, except for maybe a few TSW wheels.
If you go with 18x8 wheel, you'll want to run 235/40 tire for a flush look. If you want poke/stretch a little, then run 225/40. 18x8.5 wheel, 235/40 for almost flush, 245/40 for flush with some sidewall protection. 19 inch wheels you'll need a 35 series tire, the cross-section (3-digit number) applies the same way as above.
245 tire will only work on stock suspension, it will rub if lowered or there's a car full of passengers.