After completely trashing my tires on the salt lake, I think it is time I bought some new ones.

I have standard barrows on at the moment but am considering getting some midi's - will they make any noticeable difference? for example, an increase in traction and will they effect my speed - as in slow me down?

I fancy a set of midi's as they look nice, but the barrows will be cheaper and I don't want to affect my performance!

For those of you that don't know I buggy on a salt-lake which is as hard as concrete with a loose covering of very sharp and slidey gravel!

slick barrows are what you need. Midis will create more rolling resistance and lower your speed.

24 ply aircraft tyres

Ditto what Dino said. Aircraft tires will be uber expensive unless you have a hookup.

Midis will have more traction, more drag. They might last longer though.

For your application you may think about a knobby tire. They are made for ATV use but will fit 8" rims. From what you describe as your home surface "...salt-lake which is as hard as concrete with a loose covering of very sharp and slidey gravel..." these type of tires may provide a better solution that just slicks. Don't know for sure but I have seen others use them successfully on the dry lake beds and bragged about durability. Kinda spendy, but not so if they last a long time.