Please see below ...
1) Should I get 18 inch winter tires if I currently have 19 inch tires? I am planning on getting a tire/rim package so I don't need to change the tire back and forth. Most people do - both tires and rims are cheaper, they have a larger sidewall to protect against additional road hazards, and the overall diameter is the same as the profile is different (i.e. the speedometer still reads correctly).
2) If I order them on tirerack.com, should I get them delivered to my house and then bring them to a shop or store to get them installed? I don't have any of the tools at my house to install them as this is my first sports car. That will work - or have them delivered to the shop. You'll still need a way to get your summer tires home, though, unless you are planning on storing them there.
3) Do you recommend that I get the sensor for the tires? Yes. It's arguably even more important in the wintertime to be aware of a problem with inflation before it lets you down at an unfortunate time.
4) Anything else I should consider? Hoping to get your feedback and purchase this week. Don't run your winters too long into the spring once temperatures start warming up - you don't want to prematurely wear them out. Conversely, don't try and run your summers too long when temperatures start to drop, as traction falls off to the point of being dangerous. Consider getting tire changing tools for home - you'll save money, avoid the big lineups in the spring and fall, and get a good look at the condition of your brakes and suspension.
Also, please add your location to your user profile - you'll find it helps a great deal with the context of posts. Good luck with the purchase!