.............................................. I learned that I wanted to do more than just ride to work. Taking it on trips and running on group rides on the weekends seemed to be something I became very interested in even though I had never thought of it when I bought my first scoot. .............
This is a very good point. I know several people who bought a small bike for commuting and then discovered how much fun they are and started riding for fun. While my Super 8 is an absolute blast around town, it's top speed limits what I can do with it. It's not an issue for me because I have several bigger bikes as well.
How big should you go? Everyone has different opinions on this but I think that anything with a top speed of 70 or more will handle most situations other than long highway rides.
I also have an Aprilia Sport City 250. I have ridden it on long multi day trips with all my camping gear and have done as much as 550 miles in one day on it. Most 250cc scooters will do 75+ and can handle most highways easily. However, going 300 or bigger will have more reserve on the highway. Going 400cc or larger will also get you a much bigger and heavier bike. This is not necessarily a good thing, especially for a beginner.
Since this is your first scooter, I'd get something used and inexpensive and not worry too much about getting just the right scooter. You'll have a much better Idea of what you want after you have been riding for a while and then you should be able to sell whatever you got without much of a loss and get what you really want.