Refinancing help please

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I am needing some feedback here.

My scenario:

I am looking to purchase a 3/1 HUD at 3% down. The purchase price is $47,000 and it needs some cosmetic work and plumbing(maybe close to $20k). I plan to house hack with renting out 2 of the bedrooms at, lets say $500 a room(possibly the 3rd room as well and ill sleep in basement. The comps in the area are going for $82k.

My questions:

Is a cash out refi my best option? (In order to buy more rental props)

How soon will I be able to refi?

Is this a good scenario?

Any recommendations?