Doesn't sound like it would be too difficult to get funded.

I don’t completely understand how I could best put my money towards a rental property or fund one with the income that I am making.

I am stating out with wholesaling and once I raise enough funds will be investing in rental properties and flips.

Since the properties are in New York you have a few extra steps you need to do to keep all of your funds out of NYs hands at closing.Here's an interesting BP thread on the South Carolina property tax issue you mentioned. https://www.biggerpockets.com/forums/725/topics/604427-south.... 

Our first accepted offer was a 320 unit deal that we contracted, put up non-refundable (yeah, I know) earnest money, and thought we had our financing and money in place to do the deal.  2 weeks before closing a major (several million) partner pulled out leaving us short of the funds needed to close. 

Focus on areas with strong rental demand, like Broad Ripple, Fountain Square, or near universities like Butler and IUPUI.Maintenance Costs: Indiana weather can be tough on properties, so budget for seasonal maintenance like snow removal and HVAC servicing.Additional AdviceKeep an Emergency Fund: Unexpected repairs or vacancies can arise, so having 3-6 months of expenses saved will help you weather any surprises.Build a Reliable Team: I have lists of contractors, handymen, cleaners and property managers if you'd like me to send.Good luck with your property and future expansion!

We've seen this soooo many times in our Detroit market:(Have actually had owners choose not to do business with us because their previous PMC didn't require it - so, they thought we were the incompetent ones.Have also seen incompetent PMCs wiring funds internationally to owners - and these owners not having an ITIN, EIN or SSN!

I have a pretty large emergency fund in place for those properties, but I wonder if that capital could be better employed elsewhere (potentially acquire another property).  

I think the uneasiness comes from not having enough reserves/ funds for downpayment and closing.

We often use zoom showings, but they build on that mutual in-person experience.We don't encourage bottom-of-the-barrel neighborhoods, simply because with 60-120 year old properties capex tends to exceeed cash flow over time aka money pit.