For a track noob, you won’t be eating though tires on a 600 nearly as fast as an advanced rider, so tire cost isn’t much of a factor.
In fall of 2013 I did a track day on my FZ6 and decided I wanted to get more into it the following year so I bought a “dedicated track bike” - something that I wouldn’t have to spend a ton of time prepping/removing mirrors/luggage racks, etc, and a bike that was cheap enough that I could ride without worrying about crashing or being without a street bike in the event of a crash.
I looked for a deal on any older 600/650, ended up buying a 1999 CBR600 for $800 that ran good but had been laid down by some street squid. I spent maybe $450-500 on a set of tires, new chain/sprockets, new brake pads, and oil/fluids changed. Rode that about 6 track days in 2014 and had a blast. The following winter I put another few hundred bucks towards appropriate fork springs and a used Penske shock. Rode that the following year before selling it for a few bucks profit.
If you can afford to have two bikes, I wouldnt recommend making the FZ6 a track bike- it makes a better commuter than track bike. If you’re only having one bike, a commuter that you’ll occasionally track, it’s great for that. Every time I rode the FZ6 to work on a Monday after tracking the perfectly-carbureted CBR I would get annoyed at the FZ6’s twitchy throttle. Any older sportbike with springs for your weight would be a good choice, or you can often buy previously set up track bikes for good deals.
Which get me thinking, I may sell my current track bike come spring time, I wasn’t feeling too into it my last track day in September. It’s a 2001 CBR600, previously was a race bike, so it’s fully set up, suspension, rearsets, track plastics, etc. If I do sell it, it’ll be <$2500ish, and I’m just over in CT..