What size tyres would I need for these wheels?

check with each tire you are going to consider. They have optimum tire sizes per wheel size. Also note that often you can be faster with a proper tire for a specific wheel than oversizing a tire on a wheel. Off the top of my head I would say 11" wheel will take a 315, 8.5" wheel will take a 275.

 

8.5*18 is the std size for F355 which uses 225/40/ZR18 tires

One way to figure this out is to take the width (8.5) and convert to millimeters (times 25.4) and add 10mm. So 8.5*25.4=215.9+10=226

For the 11*18: 11*25.4=279.4+10=290 Unfortunately, this is right smack in the middle of the 285 and 295 choices--either will work. But since you are adding a lot more rear tire than front tire, you will have to adjust the rear suspension to shed grip, or add crap-loads of power; Which you might also be doing.....

 

Your total tire diameter is the rim diameter plus the sidewall heights.

The sidewall height is the width times the "series", e.g. a 45 series will have a sidewall that's 0.45 times the tread width.
The rim diameter in mm, as Mitch indicated, is 25.4 times the diameter in inches. Radius would be half that.

So a 225/40-18 would have a rim radius of (18*25.4/2) = 228.6 mm and a sidewall of (225 * 0.4) = 90mm for a wheel radius of (228.6+90) = 318.6 mm. (diameter of 637.2 mm).
That would be a circumference of (pi*D) = 2001.8 mm or just about 2 m, or just shy of 500 revolutions per Km, or about 804 turns per mile.

If you change that overall tire diameter (or turns per mile), you'll upset the torque figures, and throw your speedo/odo off.

Of course, you also have to figure both the diameter and the width when figuring what will fit in the wheel wells.
Then there's the offset, which determines how much of the wheel extends to either side of the hub center line. Add width inside the hub, and you can start hitting suspension elements.
If you go to bigger rims, you have to reduce your sidewall height by going to a lower "series" tire.
If you go wider, you have to figure both the offset and the clearance in the wheel well.

I've seen cars pull a half shaft out of the diff box because lateral stress from fatter tires exceeded the original design limits on the mechanical parts.

There's more to changing tire sizes than just bolting on different wheels.

 

Give or take half an inch aren't these 575 wheels sizes so it could be

255/40 x 18 F & 295/35 x 18 R

 

Since you are running those wheels Hoosier makes the best range of DOT race tire sizes. You can run 315 in rear and 275 front. 255 works front too but Hooiser says max rim width on 275 start at 9". We T1 racers have been doing 315's on a 10" wheel which is similarly out of spec but proven to be fast and safe on track faster than running 295 proper tire up front. So give it a try. I ran 245 as the max size up front on the 348 racecar on really stiff springs and 355c wheels. After that you need to control rub by upping the front ride height which could be a handling issue and further increase push without increase in rear ride height. I don't think a 255+ will fit. You need to consider flaring the front and going 275 because I think the car will handle better if you go that big meat on the rear I.E. too much understeer with skinny front tires. This could change because who knows where the centerlock hubs will place the rim in ultimate track width.