What would be the best front and back baskets to get for a womens schwinn collegiate 3?

I would get a rear fender (or you will have a line of mud up your back in some locales). Then I would add a rack and panniers (a bag on each side of the rack). You wouldn’t even need a front basket with panniers (I love mine). They hold papers flat and they really hold a lot of stuff. Mine are designed so that you can take them off the bike and carry them with you if you want (depending on where you are parking the bike).

Wald – made in Maysville, KY USA since 1924!

Front baskets are nice because you can watch your belongings, say a purse or small dog.

I like either the giant #157 front basket, which is bolted on
http://www.waldsports.com/index.cfm/wald157basket.html
http://www.bikecommuters.com/2008/03/13/wald-198gb-basket-installed-review-in-progess/

Or a quick release model
http://www.waldsports.com/index.cfm/wald133basket.html
http://www.waldsports.com/index.cfm/wald3133basket.html

In the back, you need a rack first, there are tons of very similar models, here’s Wald’s
http://www.waldsports.com/index.cfm/racks.html

On the rack you can put on something like folding panniers, or a basket on top, or just carry bungee cords and you can strap oddball packages.
http://www.waldsports.com/index.cfm/wald582rearfoldingbasket.html
http://www.waldsports.com/index.cfm/wald585rearbasket.html

And I agree with @Kayak8 , fenders recommended.

My bike has fenders now. woot woot. I think I am wanting a front basket and rear panniers. I really like the look of the wicker baskets. I kinda want like the collapsible panniers. I dont know which ones are good, or where to get them. @jaytkay I am going to check out those sites. Thank you.