I am a long time Little Rock investor and resident.

I assume a higher upfront cost as far as land purchase and the actual build but you would have a brand new house, instant equity and hopefully maintenance free for quite a while.

How should I think about cash vs. equity?  

It is somewhat complex to try to explain on a forum, but at a high level, you (aka GP) and your family member (aka LP) would agree on how much the 2 of you would put in for the amount of equity needed (usually expressed as a %).

Or what are other ways I can access this equity to purchase?  

Here is an example with some figures:My LLC total investment = $204,000Partner LLC total investment = $196,000Value of project when complete = $500,000Each LLC value afterwards = $255,000 / $249,000The plan was for me personally to go get the refinance loan because the terms are so much stronger than if I went portfolio with the LLC.Loan total = $300,000 (keeping at 60% or under of value for best terms from the bank)Partner LLC payout = $249,000My LLC payout = $51,000In this scenario, I am struggling to see how to get the remaining equity in the project into my personal name? 

I am looking for a Real estate equity partnership.

I think we have the option of taking out a heloc  and begin to invest elsewhere.The other idea , that I was thinking is paying off our primary residence which we owe 425k.

A property qualifies as Homestead for this exemption if an eligible owner files a Principal Residence Exemption (PRE): https://www.michigan.gov/taxes/0,4676,7-238-43535_43539-210891--,00.html#:~:text=Section%20211.7cc%20and%20211.7,purposes%20up%20to%2018%20mills.Many investors have gotten an ugly surprise when they bought a property that was a primary residence of the seller for the last 20 years.

My father is a contractor so we will be able to complete most of the work ourselves while keeping costs low and add equity.