The following sequence is presented as an hypothesis. Although there are rare exceptions, my basic assumption is that simplicity precedes complexity.
Since Passive Lipid Diffusion requires neither receptors nor any sort of ion channel, it seems to me to be the simplest form of transmembrane transport. Therefore, I would suggest that it was the first form of transmembrane transport to appear in evolution.
Both Voltage Gated Ion Channels and Other Non-ligand-gated Ion Channels allow hydrophilic ions to pass through the hydrophobic inner portion of the membrane. However, they do not require an external ligand, so I would guess that they evolved before the Ligand-gated Ion Channels.
As far as I can tell, the channels of Ligand-gated Ion Channels are similar to those channels not requiring a ligand. Therefore, it is easy to surmise that the channels requiring ligands evolved from those not requiring them.
Since ABC Transporters are more complex than Ion Channels, if complexity increases during the course of evolution, the ABC Transporters probably evolved after the Ion Channels.