Moving out of state, will be renting current home. Need help

[Buchanon Dowling]

I stumbled on this thread, and there are a lot of excellent suggestions long-term, some I was thinking about as well. I have two core questions for the short-term. First some stats:

• I own a home (my first and only) and owe 120k, it is worth roughly 200k. 4.125% with 25 years left
• I only have 25k student loan debt, no car note.
• I have just accepted a job offer in another state, and plan on renting out my current home ASAP.
• Estimates for my area show that I can rent out for roughly $1700/mo. PITI: $1150/mo.
  
• We plan on purchasing a new home (the wife insists on this) about 6-9 months after the relocation. We will rent an apartment in the new state until that process is complete.

Being that I will be >500 miles away, I will need a property manager/leasing agent etc. I really like the idea of not worrying about finding a tenant, nor dealing with any of the headaches. So, I recently found out about RentersWarehouse. If I use their services, I lose 1 month's income to find a tenant (marginally more for longer leases though) and pay $100/mo in management fees (with other benefits ofc). 

I am confident that I can pay off my student loans within 6 months using our cash on hand and excess funds each month after expenses. The issue becomes then becomes, where do I get the money for the down payment on the new house? 

Obviously, I can do a cash-out refinance on the current loan at some point. Should I do this before I move, after I move? The issue I anticipate is PMI for a year or student loans for a year after the home is built.

TLDR:
Should I wait to pay off student loans until after I purchase the new home? Should I focus on this first as planned? 

When to Refinance?

If I use RentalWarehouse services, I stand to net $308/mo in the current mortgage. Is this worth it? Any suggestions?