I used to own a 2008 GSX R750 and did commute, spirited riding, and track day riding with it. I have an RSV1000R now and honestly the GSX R750 is a MUCH better bike. Let's put insurance aside and look at the following instead:
The 750 is very close, power wise, to liter bikes before liter bikes were aiming for 200HP. For reference, the guy who owns my 750 is the one who I bought the RSV1000R from, neither of us can figure out which bike is faster in a straight line. But, the 750 is tuned with a R55 full system.
Engine characteristic wise, the bike doesn't really come alive before 6k RPM. Before 6k RPM, it'll feel like a tame Ninja 300. When the power kicks in and you're WOT, you will pop a micro-wheelie in 2nd or 3rd probably around 11k-13k. This was very consistent for me and because the GSXR750's between 2006 to 2016 have had very minor engine changes, you'll likely find the same results.
Because the bike has largely been unchanged for 10 years, you will find **** tons of parts. This is great because why do we get sport bikes? To ride like idiots. What happens when you ride like an idiot? You break things. With the plentiful parts lying around, you can fix the bike up really fast.
In terms of weight distribution, the GSXRs have a lot more weight low. This means, compared to bikes that have weight closer to the middle, your turn-ins feel a little more sluggish.
I would not be looking at a 600CC SS for street riding just because of how gutted they feel before the powerband. Also the aggressive riding positions of both the ZX-6R and R6 are ****** for long distance rides; this is specific to my body though, you may fair better.
Also, just my 2 cents on buying new, don't do it. Unless have a lot of money lying around, picking up a used one makes a lot more sense. The major difference between the different GSXRs between 2006 to now are fairings. The longest running model is between 2011 to 2017 (17's pictures look the exact same as the 2011-2016). You'll find more used plastic for 2011-2017 just because the model ran for 6 years.