If you have ethernet to each location then you can just use any router and access points. If you are hoping to have improved roaming behavior with a "mesh" system then Tim's recent articles on roaming (
1, 2, 3) seem to show that each device's behavior is more important than the wireless system in place.
If all you need is to have multiple access points sharing one SSID then that should be fairly easy with any device. You'd just want to manually configure the different access points to use the same SSID on different, non-overlapping channels.
If you're set on using AiMesh then you should be fine with any of the ASUS AC1900 models listed as supported at the bottom of the
AiMesh page. ASUS has muddied the waters by releasing many similar devices under different model names. See
this thread for a comparison of the different models. Since you plan to use multiple access points wired in throughout your home, you don't need a tri-band (AC5300) model which would only serve to use up wireless frequencies and cause interference. Unless you have a 4-stream wireless adapter (the ASUS PCE-AC88 is about the only one available) you don't need a 4-stream (AC2900, AC3100) model.