Congrats on learning to knit! You are a true charmer.
As for yarns, yes - definitely head for the acrylics. They are washer-and-dryer approved. If at all possible, go to where they sell such yarns and feel them for yourself.
Garter stitch is an excellent choice. Be sure to make it wide enough that on the truly frigid days, she can wrap it around her mouth and nose to heat the air she breathes.
Here's a thought: knit one for her... and an identical one for you. How special would that be?
And pick a color that will go with her coat. If in doubt, a dark grey/black or a creamy ivory are usually good choices. Browns, blues, and greens can be not really compatible unless the coats are similiarly-colored. Red might be another compromise color to think about.
Good for you!
PS - if you use large-sized needles, the scarf will feel softer and poofier. Say like size 9 or 10, with knitting worsted weight [4-ply].