My plan is to sell my primary home in New York and purchase a house to live in South Carolina.

We lived in a little apartment above the garage and rented out the main portion of the house. 

A furnished mid-term rental or month to month lease can be well worth the small incremental monthly cost for this flexibility if you are serious about finding a great live in flip candidate on your timeline, not that of your employer's. 

Very generally speaking the areas of Hartford and New Haven where you can hope to attract qualified tenants (assuming that is your goal) are very expensive because most of the people with something to lose that live in these cities generally live in 2 or 3 areas.

If not, do you own the primary home you're living in now? 

They knew a dog lived there when they rented it and they rented anyway, knowing they had allergies and chronic asthma they rented a home with carpet. 

My client's living room is completely unbalanced and odd looking because this wasn't done, which I had to hide with some fancy drapery "magic" that was expensive.

This may be controversial but it seems like you would be saving a lot of money at the moment given your reduced living costs.

We overthink real estate...Just find a place that people with options want to live. 

Additionally if you are deeding the property you live in to an LLC you may lose the homestead exemption which could actually increase your taxes.