I dunno if the weather where you're at permits it, but the best thing I ever found for making tunics was heavy cotton gauze. Not the lightweight bubble gauze stuff (that makes pretty chemises but isn't up for much else) but the heavier stuff that's meant for making summerweight women's suits.
For winter/cold spring wear, I used to make tunics out of poly/rayon gabardine. I know you're not supposed to use poly, but for the sort of 'entry level' garb you're talking about, it's really not a bad compromise. It's usually fairly inexpensive, it holds up to a beating (when I was in the SCA I was sewing for two adolescent boys) and it's yummysoft and warm.
For trimming basic tunics, my favorite thing was bands of 100% cotton twill tape (
Denver Fabrics sells it in lots of colors, some fabric stores carry it but some only have poly/cotton). It's cheap, it's forgiving to apply, and it's a lot more authentic on a peasant-ish tunic than the beautiful jacquard trims that are so tempting and spendy...
Also, if you're thinking of going to a later-period persona (specifically if you and/or your daughter want to wear those nifty bodices), I have a
set of instructions for making up a non-authentic but quick and easy chemise, skirt, and hat set.
I hope this helps, and good luck!