Wool is definitely the way to go, but it's more expensive. And you can't just throw it in the washer/dryer when it needs a cleaning.
Are you in an area with really cold winters and/or do you ride at night? Since it sounds like your girl gets pretty sweaty, if it's really cold outside, you may want to invest in a nice cooler (and one that goes all the way up her neck like the one you linked). You could look for a used one to help save money.
Wool is the best. And seems to work better in my experience.
Fleece is cheaper and easier to care for.
I haven't had experience with Irish Knits...I own one but have never used it. It's doesn't seem as cozy as fleece or wool.