I guess the courses are seasonal.... don't see anything until april
They are seasonal but I would definitely get on the schedule and do it. The RE course taught me a lot about the mental approach to riding and what you should be looking for. Basics and fundamentals that were always in the back of my mind on the street, but also paralleled a lot of the principles that are reiterated during the inital classes for people that start doing track days. This is to say it's not just some stupid course you 'have to get through' to get a motorcycle license. There is value in it for sure.
You don't need to start on a small bike, that's all bs. My first motorcycle was a naked 700cc. I've ridden dirtbikes, dual sports, naked bikes, baggers, modern cafe racers and crotch rockets. You asked about the comfort of a sport/supersport - if that's what you want to buy you''ll be fine comfort wise. If you can ride a road bike for hours at a time, you'll be fine on a crotch rocket. It's different than a bicycle, you're gripping with your knees and core. The more important thing to try to figure out is the style of bike you want. It's really not possible to know what to get until you've actually started because where you ride / who. you ride with will be a big influence on what you enjoy doing. If you get an SV650 (great starter bike) but you start riding with people who are all on crotch rockets, you're not going to enjoy it. If you've got a crotch rocket and everyone you ride with is on cruisers then the same applies. If you just want to ride around by yourself and cruise then it doesn't really matter what you pick - just ride.
If I had to do it all over again my first bike would have been a 600cc supersport. It has nothing to do with speed You can go fast/slow or ride safe/wreckless on almost anything. I say this because there will be more people riding supersports for you to ride with. I know 2 groups that still go out every weekend from central NJ to upstate NY and ride the Bear Mt / West Pt area. Man I miss those rides.
The other thing to consider is what JDog mentioned. If you have any inclination to ride dirt (so much fun) then a dual sport is where it's at. They aren't really fun on the road if you want the full motorcycle experience, but to get you to and from trail systems (if those are options around you) it's hard to beat.
Good luck!