[will.c]

very good question OP, I got a lot to say so bear with me. You and many others may know some or all of the following info already, but I'm just gonna clarify everything for those who don't.

First my credentials quickly: Daily drive 20k/yr; 15 DE days/yr; owned 4 diff sets of wheels & tires (snow, daily, track); current setup = 17x7.5 on 205/50 Wintersport M3; track setup = 17x8.5 Kosei 245/40 Star Specs; daily TBD in spring.

Next, a few answers on some potential theory questions:
Q: steering quickness drops from 19" to 17", in addition to now having blizzaks?
A: both valid.
Q: what determines the steering quickness/sharpness/response the most? (in terms of wheels and tires only; no suspension or any other variables)
A: tire's sidewall stiffness. Well, of course that 19" will have better response than 17" given identical tires, but what I'm saying, for example, is that 17" with RS3s or Star Specs will be stiffer than 19" with DWS' or V12s. In addition, tire pressure plays a (significant) role here too, so 17" with stiff tires and jacked up pressure, you'll be on rails.
Q: why race cars use 18" or even 17"?
A: lower "moment of inertia" (equivalent form of "mass" in rotational sense, hence plays a much bigger role in every aspect of a moving car than simply mass). (1) As stated above, steering response can be made up by type of tire and tire pressure, so there's no need for 19". (2) typically for same wheel design, larger diameter = larger mass = much larger moment of inertia. (3) assuming 2 different wheels have identical mass at different diameters, the smaller diameter will have less moment of inertia because majority of the mass of any wheel is at the barrel, not at the spokes. (There's also tire weight/moment of inertia to consider and compare to the wheel size, but let's not get THAT far.)
Q: then why don't all race cars go as small as 17", 16", etc?
A: race cars typically have large brakes that will require minimum of 18" for clearance. If they could go lower, they prob will go lower. Some, not all, 17" will clear 335i brakes.

What I recommend you:
Since you're function over form, budget-conscious, and need to be able to daily-drive (such as I on all three), my short answer would be Apex ARC-8 17x9 ET30 w/ 245/40/17 Michelin Pilot Super Sports.

Long answer: I'm sure there are other cheap, strong, light wheels, but I just don't know/remember to list them out for you. But ARC-8s, for one, are pretty strong, relatively cheap, don't need any spacers, light, relatively-high resale value, etc. I got Kosei K1s but I don't know if I'd recommend them for the streets. I've heard some stories. Yes, they are relatively weak, so streeting them won't be a great idea. Afterall , the most wheel damages are done at the street (potholes) rather than at the track, which may be ironic to some people.

Super Sports are light, great grip (just a tad bit lower than Star Specs, RS3s, or RE-11s, but these compromise streetability a bit too much IMO), excellent life, comfortable (yes, sidewalls are softer than the aforementioned three, but you can mediate that by jacking up the pressure to about 40psi when you go to the track), predictable and controllable at the limit, AND they are fantastic in rain. I believe you can typically fit 255/40/17 on all four, but unfortunately Super Sports are not available in that size. 245s are good enough.

Don't get use tires. Risk of apparent or unapparent damage is too large to be spending (significant) money on something that determines the car's characteristics the most, especially if you're an enthusiast expecting to push the car to the limit (at the track). The piece of mind of fresh tires is well worth the money.

Used rims? I'd say a hit or a miss cuz a lot of times people say they are not bent when they actually are, as well as other more critical things. But if you can inspect thoroughly, and the deal is good, then go for it.

Now, whether to get a square or staggered set is a whole separate story. Quick answer on that would be square IMO, but there are benefits on both, and I can elaborate if desired.