+1. When you fall from a two-wheeler going 45 mph, the pavement (and any other hard and immovable object you collide with) isn’t going to care whether your ride had 10" or 18" wheels. And definitely take the MSF course first. What they teach there is completely applicable to riding a scooter: watching for left-turning cars, knowing how to execute an emergency stop, leaning on turns and countersteering, etc.
There is a wide range of scooter types these days, from the traditional small framed, small engine and small wheeled scoots with a manual transmission, to “maxi-scoots” with 500cc or 650cc engines and as large as 16" wheels and CVT (twist-and-go) transmissions. It sounds like your primary reason for going with a scooter is for the mileage over a short commute, so a 150cc sized engine and a CVT transmission would be a standard configuration for your needs. If you would like the option of going faster (highway speeds) look into a 250cc or bigger scooter.
I myself currently ride a Piaggio BV500 for my commute, which has a 16" front tire and is capable of going at least 80mph on the highway (which I have done) with power to spare (not that I have often done so, but it’s nice to have the option). They cost a fair penny when new ($6300 MSRP), but I got a used one with 1400 miles on it for $4700, not a bad deal. In contrast, a used Vespa GT200 (a 200cc “modern” CVT scooter with traditional styling and 12" wheels) would go for around $3500-4000.
The next question would be how much you want to spend and what kind of styling you want. There are “mail order” scoots that are very cheap but have a reputation for poor build quality, while “name brand” scooters like those from Vespa/Piaggio, Honda, Suzuki or Yamaha (just to name a few) will cost more.
BTW the same advice for a new motorcycle rider equally applies for someone whose first bike is a scooter: think about getting a used one to use for the first couple of months, 'cause you are likely to do something stupid that dumps the bike, like getting the kickstand/centerstand thing wrong at a parking lot or gas station, or using too much front brake while going around a curve/turn at low speed, etc. Or else resign yourself to the thought of scratching or denting it eventually.