The first thing I would do is make the improvements that you're talking about to your primary home. The improvements you're talking about probably won't make a huge difference, but it might slightly increase the appraisal value when you go to refinance. Note here: since you will be making this a rental, make sure you leave some equity in the property and don't overleverage it. Also, make sure it will still have a decent amount of cash flow with the new payment. I would say refinance here because you will be using most of it to leave in an investment long-term (down payments)
Then you could move onto either of the 2nd or 3rd options. I might recommend buying your next house to live in. That way, you could get your feet wet renting out your first house before diving into multi-family.
I would say to use traditional financing for the purchase of your next home.
The financing on the multi-family depends on whether you will be buying something turn-key or something that needs repairs. If it is turn-key, I'd go with traditional financing, and if it needs work, you could do some variation of a BRRRR.
Hope this helps!