My gym bag is by Briefing, US-made, heavy-duty nylon, I think they make for the military so it's fairly hefty stuff.
 quick check, it's the "gym wire bag"
If you want a classic cotton blend hoodie you're not going to get much rain protection. You're more likely to find that in some sort of softshell jacket--full REI/Patagonia territory.
This Pedaled softshell has been tempting me as an alternative to the standard outdoor brands, and it's on deep sale at East Dane. Oh fuck I just talked myself into it.