GL with the eibach pro kit... you should definitely see an improvement in handling but generally eibachs are pretty soft among lowering springs IMO... I think you'll see the benefits of lowering, but not really any benefit from increased spring stiffness (at least I'm guessing off the top of my head) Should be a very good choice if you want a similar-to-stock ride
I think with a good alignment and that setup you'll be very happy!
The last major factor is tires, and how long you want them to last. A good UHP tire has a crazy amount of responsiveness and much more outright grip. Depending on how many miles you drive per year is what I'd let determine the kind of tires you want. If you want tires that will last 40-60k you'll probably want a "high performance all season", for ~30-40k you can get a good "high performance summer" and for ~10-20k you can go with an ultra high performance tire
Examples:
All season: Falken Ziex 512, Kumho Ecsta Whatever
Summer: Nitto Neogen or BF Goodrich GForce Sport
UHP Summer: Falken Azeni, Dunlop Dirrezza Z1 Star Spec, etc
For the characteristics you're looking for, you want to stay away from any tire that advertises "smooth ride" "quiet" "luxury handling" or "touring"... don't worry about trying to cram a wider tire on your stock wheels, stock size or slightly larger should be fine. Going to a summer (if you are running all seasons) or a UHP summer would be a huge difference in grip... just realize if you go for UHPs you'll probably be replacing them every year (fine if you autox as you'd replace them anyway)