Tunica (Nova Roma)
You may have short sleeves, approximately 6" long by 12" high, cut with the body panels, but sleeveless tunics may have been more common.
Round necklines were known, but apparently the usual neckhole was a slit about 20" long, made simply by leaving most of the shoulder seam unsewn. For heavy work the right arm can be slipped through this neck slit. To close up the neck slit so the tunic will stay on your shoulders, gather a "knot" of slack fabric at the back of the neck and tie a cord or thong around it, or just pin the slit shut with a couple of fibulae.
The tunic hangs to the knees or below, but is normally worn bloused over a cord or tied belt to raise the hem above the knee.
Practically any available white or off-white is acceptable; it need not be blanket-weight, but should certainly be 100% wool.
Undertunics can be made of white or natural linen, the same shape as your wool tunic. In very hot weather a linen tunic may be worn instead of wool to avoid dangerous overheating.