I'm open to using a conventional loan during the refinance stage. 

@Armani Diaz is this a conventional loan or non conforming?

Then, you could either use that money to fix up the property, or use the leftover money to purchase another property with a conventional loan @ 20-25% down.

Details:Goal is to Owner Occupy Location: Type A *very close to great schools, downtown walkable locationHouse: 4 Plex 8 beds and 4 bathsSq Ft: 3,548Price: $425,000Mortgage: 20% down 30 year conventional Current Rents: 790, 985, 945, 910 per-month  *These seem low for this area and for the condition of the unitsOccupancy: 1 will be open for new owner to occupyInsurance: $180 per-monthProperty Tax: $415 per-monthAnnual Maintenance: $800Water, sewer, garbage, electric: all paid for by current tenants Cap Ex: $280 per-monthVacancy: $280 per-monthProperty Mgmt: $345 per-monthThe property has had many Cap X improvements over the past 6 years including, new roof, windows, refinished hard wood floors, paint, foundation work, plumbing, electric... 

In order to have extra cash to help me pay off my student loans, I just wanted to explore the idea of using a hard money loan in order to finance my first deal and then later refinance it into a conventional loan. 

Unfortunately, I am kind of a dumbass and didn't realize that a conventional loan has to be the purchase price, something my realtor missed :/ I was under the impression that a 203(k) vs conventional with borrowing for rehab would be like the difference between a 3.5% down Conventional, and an FHA. 

If you have two FHA loans you will not get another one until you refinance one of them and convert one to a conventional loan. 

Can anyone advise me as to the minimum down payment on a conventional investment duplex?

Conventional.

Conventional 20% down How did you add value to the deal?