Which plan do I need to be able to file with a 1099-NEC? Will +PLUS work or do I need to purchase the deluxe or premier?

Online program ... you need at least the Deluxe or Premier version to enter the income however if you have any Sch C expenses to enter then you must use the Self Employed version.

Downloaded version ... ANY of them will work ... Basic if you don't need a state return, Deluxe or better if you do need a state return.  

Plus is not a software version.   PLUS is just an add-on feature that gives you access to customer support.   If you have self-employment income on a 1099NEC then you need either online Self-Employed or any version of the CD/download so that you can prepare a schedule C for your business income and business expenses.

https://turbotax.intuit.com/personal-taxes/online/