can't speak to Doug Polen's school, but it's 'free,' right? Go have fun, and play it ultra safe so your bike stays shiny
Bike advice really depends on your goals, preferences, budget, etc. You only specified a budget.
If learning is your primary goal, an SV650 teaches you a ton about corner speed, without having overwhelming power to get you in trouble. You could get a NICE sv with all sorts of suspension and other upgrades for $5k. SV's are also cheaper on tires, because they run a 160 rear, and don't power through them quite as quickly as a 600, 750, or 1000.
If you like the high-speed stuff, a 600 or larger might be a better call. I tend to believe you can stay on a 600 longer, but patient riders on SV's have certainly taken them all the way from "B" to "A." the "B" group passing rules can get frustrating on a less powerful bike though.
you'll know after your first trackday, but one big question is how you feel about the engine-braking of a twin. I hated it. Moving to an I-4 made my life a ton easier. Some people are addicted to the torque coming out of turns though. the selection of 600's in the $5k range should be great. Again, you'll get a nicely set up bike for $5k, but probably slightly older or higher mileage than a similarly priced SV.
If you know you like high-speed stuff, and you'll be on big tracks, don't overlook a 750 or a 1000. They do eat tires more quickly, but a big straightaway can make even a 600 feel slow.
good luck with your decision.
