Yes ... get a jacket that is "waterproof breathable" with pit zips already there.
I posted a link to the Groundeffects jacket I wear ... it has a hood. It's $299 NZ.
MEC has a couple jackets ... you could get one for $172.
Cycling : Clothing : Women's : Waterproof-breathable - Mountain Equipment Co-op (MEC). Free Shipping Available.
Wait ... your budget for a waterproof breathable jacket is $50?
Well ... maybe you can find something that will do for now from Nashbar ...
Nashbar - Cycling Outerwear / Raingear