I appreciate the advice! I hope you all don't mind a little more backstory.
I have a very good relationship with my Dad and he's gotten involved in financing real estate deals for my brother, but I tend to agree that these arrangements should almost always be avoided. My Dad brought it up in part because he wants to see me my pursue my passion (woodworking/furniture building - I want to quit my desk job and do that full time in the next 5-10 years) and he's seen my basement/current garage setups and found them to be pretty limiting.
The garage currently lacks a foundation (built in 1890) and I have a few workstations/tools set up on some very wavy, uneven surfaces. It's built on an incline and the floor is basically built like a deck is. 100+ years later, there has been significant settling and wood movement. The inspector initially said I need to tear it down ASAP and just have a parking slab poured for now.
My desire to finance as opposed to paying cash to incrementally build it little by little is because of the rent that I could start getting rental income right away - as opposed to outlaying thousands and thousands of dollars to pour a slab, build out the garage, and chip away at finishing the apartment. Those thousands wouldn't be making me any money, and the cost of not financing would be ~$12,000 X however many years it takes me to complete it.
That being said, I haven't looked into construction loans much yet. I guess I didn't think of it because it struck me as more of a remodel type situation and those loan terms are really bad if you don't have much home equity. If you all suspect I could get a favorable loan situation by seeking a construction loan, it's probably my best option.
Thanks again for all the feedback.