Whenever you mention cleaning to someone, their reaction is normally to run for cover.
You don't have to do a deep clean after every time on track (I do though, I'm a bit OCD!), but its important to give things a wipe over.
Because you don't want to get to your next track day and find an issue that you would have picked up by having a look and a wipe around your bike.
If I'm honest I have a good look around the bike after each session, even if its only for one minute. I don't want to head out for the next session with something leaking or about to fall off. Track bikes take a hammering, its easy for a peg to come loose, especially on the shifter side.
I quickly check for oil, water and brake fluid. I can then go back on track knowing the bikes as safe as it can be and I can concentrate on my riding.
Only clean your chain with a chain cleaning product, I use paraffin. Some products can remove the grease which is meant to stay behind o-rings. When lubing the chain be careful not to get any on the rear tyre.
Some people have discovered that some household bleaches/Limescale removers can bring stainless exhausts up like new again, but after seeing what Harpic 10 did to a set of headers when left on a little too long, I'd rather use a stainless cleaning product and some elbow grease. You decide.
To clean the brakes I only use brake cleaner (it's in the name...) I would highly recommend that you buy a pressurised pump sprayer and the cleaner in a bottle. Its far better than spray cans and you actually end up using less as you get more pressure with a pump.
Microfibres are a good investment too. I get a 36 pack from Costco and they last me ages, you can even wash them.