This protects you if the lender/seller passes away or would try to sell the property out from under you and your seller finance agreement.

if the tenant still refuses to vacate , what can I do to protect myself of the for an eviction?  

LLC is for asset protection NOT for tax benefit

Negotiation Skills: Whether it’s negotiating leases, handling vendor contracts, or resolving disputes, strong negotiation skills can make a significant difference in operational efficiency and cost savings.In my experience, a property manager who excels in these areas not only helps protect your investment but also maximizes its profitability.

What do you suggest is the best entity classification to choose from for a new, up-in-coming business owner to get the best balance between liability protection and tax advantages? 

To address potential future problems, wouldn't a homeowner's policy and/or home protection plan cover any occurrences?

Asset protection.

My very limited understanding is that the mortgage being in your individual name and you operating the property through a single-member LLC makes piercing the corporate veil fairly easy and that insurance coverage is typically a better protection plan.

An LLC will do nothing for you such as providing asset protection and shielding you from lawsuits.

@Avi Lah the PMC's alleged liability is immaterial as it does NOT protect the owner.An owner must sue their PMC and prove their liability.