Hi Christopher, congrats on taking your first steps on your REI Journey!
I took the same route as you, converting my primary into my first rental. While it was still a primary, I ReFi'd into a 1st position HELOC. That allowed me to get the primary residence rate, and access up to 80% of my equity. Along with that, I no longer had a mandatory monthly minimum payment, just an interest only cost. It allowed me to really wait and find a well qualified/good fit tenant. It's been great, I'm cashflowing well and I can write a check from my line for an additional property purchase at any time.
Your concerns:
1. In my experience, you shouldn't have much trouble moving to an LLC regardless of loan type.
2. Depends on your lender/underwrite. A strong lease will definitely help, but without past rental history it may have any impact.
3. Definitely always good to have some money available as as safety net. Heloc is a great option because you only pay for the cash if you need it.