You need a monitor too? Then I suggest waiting till you have atleast $500 to spend on the tower. Anything lower than that you are just not be able to get satisfactory experience.
Also why do you want to record at 60fps? Why not 30fps? You can game on 60 but record on 30.
Just tell me yes or no if the parts I picked will record minecraft 720p at 60Fps.. I heard the integrated graphics with the a10-5800k run minecraft high settings around 120ish without recording so idk