Kumho KU36 vs. Toyo R888

KU-36 is a street tyre, not an "R Compound"
 
Toyo R888 is an R compound, which will have a much lower treadwear rating so it depends what you're planning to do with the car.
 
they are both fairly old designs so be sure to check the build date of the tyres.
 
in my opinion the best affordable street tyre around at the moment is Federal 595RSR  (contact dylmart/Gorilla industries for prices) 

Thanks for pointing that out Sinbad, just to clarify they will be a dedicated set of track tyres, I have separate ones for daily use.

You may want to look at Nitto NT01's for track use.
The Nitto is a r888 compound with stronger side walls and different tread patten.
They are cheap($1000 a set), wear very well, come up to temp within 2 laps, are consistant with grip(up to ten laps tested), only 2 seconds slower than 6 other cars on slicks(at Winton Super TT round) so enough speed in the tyres to have a good time. They are well documented by BMW teams in the U.S. with good results for the money spent. They are not as quick as the top brands but for 50% of the cost its not too bad. I would like to try the Federal's but I have two sets of Nitto's for the same money. The Kuhmo's are on special atm. Another good tyre.
 

I notice that in NT01's, Nitto list a 205/50 R15 (ok for the fronts)and they also list a 225/45R15.
How would a slightly smaller rolling diameter rear go for track use?  (4 percent gearing difference to stock).

180Shauny

Well it would mean your engine does higher revs for the same speed right?
I'm nowhere near topping out on the straight at Phillip Island so should be okay I would think.

Correct, 4 percent higher than with stock size tyres.
Might suit some tracks better than others.
 

I dont think the gearing would make any real difference, but what happens to the ABS when only one axle has a significantly different diamater?
 
I know on gtr skylines, this causes the 4wd system to behave differently to normal, as the ecu thinks one of the axels is starting to slip due to different wheel speeds.
 
Cheers
 

true re ABS comment.
 
One of the guys here Smokey (RIP) ran 225s all round on his race MR2, which was very successful.
 
Cheers