Not knowing your the new # of pc and servers that you are currently running I would at at least try and get two people in the door. One person would have to wear two hats in this can. You stated that you like ot have a network and systems admin try and find a person that can do the job of both jobs for now and a hire a help desk person that can also do the job of a sys admin. I would write it up to the executive staff that you would need that one person would help with the new demands of a new infrastructure, the network/sys admin, and that you would hire a more advanced person on the help desk side, helpdesk/sys admin, to help with new user demand.
Document they change in demand on the old going into the new infrastructure now so that if need to hire one more person all you would have to do is take your network/sys admin and make them your network admin, your helpdesk/sys admim you full time system admin and then hire another helpdesk person. All of these would be lateral moves and might keep the exec staff of your back when you ask for the new hire within another 6 to 12 months.

Good luck