Assuming you intend to feed this antenna with coax, you need some kind of balun to prevent common-mode currents on the feedline which will degrade the directionality of the antenna. There are many kinds of balun that would work. A bazooka balun or a choke balun are two of them. The balun may or may not also have some impedance matching capability. A gamma match and folded balun are other options. There are many more.
For an antenna with this many elements the directionality should be high, so common-mode currents must be very small to avoid significantly degrading the pattern. You might want to measure the common-mode current and add additional choking if necessary.
The feedpoint impedance is best determined empirically or by modelling. However it is generally true of Yagi antennas that the impedance is lower than 50 ohms. A gamma match is easily adjustable. If you can measure only the SWR but not directly the impedance, this gives you the option of finding a good match by trial and error. If you have an antenna analyzer or similar which can measure the impedance, a lumped element match or a stub match are other options.
As you can see, there are many engineering decisions to be made besides the dimensions of the Yagi elements. The feed of an antenna is an important and often neglected aspect of design. Neglecting the feed you will end up with an antenna which works, and you will make contacts, but it may not work to its fullest potential. It may not even work better than a simple vertical.
If you have a taste for experimentation, then by all means build this antenna and experiment with feed options. If you're anything like me, the experiments are most of the fun and the antenna might not actually be done in a year. However if your intention is to get something working immediately, consider a simpler design which includes all the feedpoint details, or a commercial antenna that requires only trivial assembly. You may build the simple design, and then when attempting a more complex design such as this you will have something for comparison, and you can judge if adding 8 more elements made an improvement.
