I was involved in a travel plaza that was at completion 15 million. 

I am looking into purchasing a 20 unit apartment building in Cleveland that has been completely renovated.

As a rental investment it is not worth the risk or work load based on you having negative cash flow unless you are in a high appreciation market and willing to gamble.SFHs make for poor income property investments and are primarily a appreciation play.

@Jason GottThat is completely understandable and wise to be cautious.  

I'm from CA but currently in North Carolina completing an internship, and this is my first time on the east coast.

have always viewed RE primarily an inflation hedge. 

I'll agree with @Ashish Acharya here: if you're wanting to sell the property primarily as a way to get some tax-free cash, then yes, sell within three years after moving and you qualify for the $250k(single)/$500k(married) Sec 121 exemption.

I've had a "shell" of a website up for quite a while now and I hem and haw about completing the project so it is fully operational, mostly because I'm questioning its true value. 

We completed one flip together that resulted in profit.

But the short answer is there likely is a way to meet you objectives while completing a 1031 exchange which also preserves your option in the future to continue to exchange real estate.