Rehab and Stay? Or Rent and Buy Another

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I'm brand new to the game so all of this is new to me.  I'd greatly appreciate any advice.

Currently live in a 3/2 that I am 50% Joint Tenant in Common with a sibling. Getting ready to buy the sibling out by cash out refi and quit claim deed. I'm taking an additional $15k out to rehab the home (new windows, A/C, and a bathroom). My question is... Should I take out an additional $20k for a down payment on a rental property (SFH) or do I rent the house I'm in and go buy another house to live in with an FHA (3.5% dp).

Welcome all responses and reasons why.