Also directivity/sensitivity. While turn count will improve overall sensitivity, loop size will increase directivity. Keep in mind that both loop size and turn count affect probe filtering characteristics (it IS a filter), so I highly recommend experimenting with several designs. Have a look at my attempt at making magnetic probe from RG174 [3]. It is fat because of two layers of thermal shrink tube, which made it stiff enough for my experiments :)
It is hard to tell from a picture, but it should be that this probe uses two wires exactly for this purpose: one acts as a central conductor, other as a shield.
[1]: http://www.compliance-club.com/archive/old_archive/030718b.j... [2]: http://www.compliance-club.com/archive/old_archive/030718.ht... [3]: http://imgur.com/hiRUJl6
Both may be correlated, and both gives you side channel information to attack cryptography.