Apart from UEFI booting issues, all modern motherboards should just work with Linux. The most common hardware problems apart from UEFI are graphics and wireless, but in your case the motherboards will not cause such issues since there is no graphics controller or wifi chip on the motherboard itself (the VGA, DVI, HDMI ports, etc. are to be used with the CPU's integrated graphics).
As for UEFI, MSI does not appear to cause much problems here on the forums, nor does ASRock. All three boards should just work when building a new Linux Mint computer.
I don't think it really matters which one you choose. The ASRock H77M has two more USB ports, and two native SATA 600 ports (B75 boards have one native SATA 600 port, and in the case of the B75 Pro3-M additional ports provided by Asmedia or Marvell chips). The MSI B75A-G43 has more room for expansion cards. Apart from that, they are mostly the same (same sound & ethernet chip, for instance).
Registered Linux User #528502
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