That's the problem with being in uncharted territory...you don't know where the heck your going...
I don't know much, on account of I haven't been to the track yet either, but....
I was told I should have at least two pulling gears (3 or 4 is better) for/depending on track conditions dry/slick or moist and sticky...so I would keep 2nd in mind as well as 3rd...(you may need to change gearing "in" the 820 to bring them closer, make them both useable)...
My driveline is set up for 6500 rpm with a fairly stout motor and we're running basicly the same size tires...I'll be running either a 47.5:1 or 40.5:1 final ratio...you can do the math from there....
Why did you pick 4000 rpm for motor..? will you be running goverend ?? how "built" will this motor be...? At that rpm my guess is you may want to be in the 30s:1 final ratio, but I'll let the more experianced guys chime in...