If you want to learn the basics of FPGAs, it's best to get yourself a Nandland's Go board. It's cheap ($65 I think) and very basic, but it's accompanied by very good tutorial videos which explain all basic blocks of FPGA (LUT, FF, BRAM, etc.), how they work and how to use them. As an added value, all tutorials are provided in both Verilog and VHDL so you can pick the language you prefer. I recommend you to watch these tutorials even if you don't want to buy the board as they are very good general introduction.
Once you're familiar with basics, download AXI-Stream specification (google for "AMBA AXI4-Stream Protocol Specification") and study it thoroughly. Try implementing a very simple AXIS master and slave just to get a "feel" for how it works. You can use your Zybo board to verify these in HW. For your project I think you can get away with AXI-Stream master endpoint (connect it to DMA engine), which is very easy to implement.