I prefer a decent foam brush, but I don't see why a pad couldn't do as well.
Since you have a large area, you will need to get the finish on and leveled out and uniform over the entire surface as quickly as possible, at least for the finish coat. To get real time practice, using a foam roller, get the finish over the surface uniformly, after that is done, use the pad dampened with finish to level the surface, getting rid of the minuscule texture left by the roller. Let dry the recommended amount of time before sanding with 240 to 320 grit, getting the surface satiny smooth. Then, since you now have a better feel for getting the finish over the surface, set a lighter, but complete coat over everything again and level out one last time with the pad.
It is important to not let the finish to start drying wile applying the finish. The term "wet edge" is used a lot in this type of finishing. You could use a pad exclusively, but you would need to watch how you apply so that when you start applying finish beside a part you did a few minutes before, depending on the conditions may have started to dry and then the finish will show a seam (lap) there. So get it on the whole surface quick to alleviate the lap made by not maintaining a wet edge.
You could go a third coat since it is a wear surface, but for the sanding, use only 320G since the surface will be really smooth by this time.