First, you made a wise decision to forgo the experience of dragging yourself off a plane, sleep-deprived, completely exhausted and jetlagged, then jumping in a car to speed off on the wrong side of a road in a foreign country (what could possibly go wrong?). Yes, take the bus to Galway, it's perfectly comfy (you may catch some Zs) and the right choice. I don't recall which company we used, I suspect it won't matter much. It could not be easier. Exit the terminal, follow the signs to the bus, walk a few steps (it's not far), find the right bus (easy, good signage), pay the driver for a ticket, get on bus, settle in, bus rolls out soon enough. Few travel experiences are less demanding.
I'd question the (very short) length of your trip (there's so much awesome to see and do, you will wish you had more days), but that's your choice.
Torn between the Cliffs of Moher versus the Aran Islands? Good news - if you go to Inis Mor and do a little walking, there's no need to go to the cliffs of Moher. Read this old thread:
Separate day trips to the Cliffs & Islands?
Now, time spent on Inis Mor may not be terribly enjoyable in a driving rain storm (you'll be out in that rain most of the time you're not huddling in the pub), so if it's stormy you might prefer a long bus ride to the CoM as you watch the rain pelt the bus windows (you'll be out in it for only a few minutes). If it's not raining, I'd skip the famous cliffs and go spend a night (two if you can manage it) on Inis Mor.
If the weather is good, I'd ditch everything else, head out to Inis Mor and spend a night or two (if you go, take the plane, not the ferry: outbound, take the first flight of the day, when returning take the last flight of the day...this "buys" you more time on the island. The plane is cheap, tiny, and utterly thrilling...they make the hop to Inis More at "treetop" level, it's a hoot).
If it's raining hard, you will probably want to be inside (a bus, a warm pub, something, anything) so maybe stick to the mainland if you are not lucky with the weather. That (the weather) is part of the bargain you make when visiting this very green, very moist place in early March. Hope for clear skies, prepare for something less, keep your fingers crossed and remember all those old saws about "the luck of the Irish."