Thank you both for your informative posts and support to the FPGA community. Please find below more background on my questions.
I have no experience in FPGA design and development. My primary objective is to buy my first FPGA board to learn the basics through examples in Verilog/VHDL. The board is not meant to meet all the requirements of the business/production applications mentioned. My objective is more to invest in a board that will allow me to progress for some time and ideally design small projects/applications. The wide range of potential learning projects applications mentioned is coming from my education background in ECE (digital signal processing, communications/networking and machine learning) and my professional experience in quantitative finance and financial markets.
Of course, the choice of the Nexys video is not definitive and your expert recommendations are very much appreciated. From the reviews on different forums, the Nexys 4 seemed to be a good FPGA educational board. I thought that the Nexys video would give me enough capabilities to design small experimentation projects/applications in my areas of specialization. The purpose of my novice technical questions were also to assess the potential limitations/scalability of this kind of board and more generally the IP, licensing and hidden costs.
Answering your question: "Why do you believe that an FPGA is necessary or even appropriate for your particular efforts?" I am not sure if the FPGA will be appropriate for my efforts. What I do know is that most of the algorithms, simulations, models and classifiers I have designed or worked on are running on FPGAs now with significant acceleration/latency improvements. Of course, ultimately if I decide to develop business applications on FPGAs, I will make sure to assess the requirements and I might certainly not do the design myself.