I'm very sensitive to synthetic fibres, I get very hot very easily. Therefore I tend to stick to natural fibres where possible. I try to line with silk when I can find it at a reasonable price, but if I can't, and it needs a silky lining, I use Bemberg/Cupro lining.
It has a much nicer feel than Acetate or polyester, added bonus is it irons beautifully and less likely to melt under the iron!
They use Bemberg a lot in men's suits and waistcoats, or at least in the nicer ones (I'm sure the cheaper ones are poly).
I can't feel the difference between Bemberg and natural fibres for breathability.
To save yourself some meterage you could line the bodice in cotton and the skirt in Bemberg?
Hope that helps!