I run that same tire on those same sizes and same sized rims, I love it. 225/45/17, go for it! If your tire mounter whines about the stiff sidewall and width of the tire and wheel tell them to suck it up
That is an approved wheel width for that tire according to tire rack.
Other extreme 200TW tires are faster (and more expensive... Rival-S, RE71R - I have heard many reports they are faster than Nitto Nt01 and other 100TW "R" compounds, albeit only for a few laps until they pass their optimum heat range - they heat up very quickly which makes them great for autocross and time trials) but they heat up quicker and wear out waaay faster, the R-S3 loves heat and lasts a long time, and in my opinion is a good "First" HPDE track tire.
I like to run mine 36 hot in front and 38 hot in rear, which means checking the temp before a session, then immediately after, and noting the delta, then before your next session checking again and seeing if you need to bleed a little out as the day heats up. Caution - don't bleed out too much and go out with underinflated tires. Once you get it right there is minimal bleeding involved, usually after the first session or two in the morning. And don't forget to add some back in at the end of the day before driving home, *or* for sure check them the next morning after they have sat all night...
If they get over 40 hot they will feel greasy and you will slide around a lot. Run them too low and you will tear them up, especially the outer edges.
I like to start at 32F/34R and see how it goes throughout the day.
Great HPDE tire