Currently you can only choose from one of ShopSite's real-time shipping quotes options, i.e. one of either UPS, FedEx, or USPS. If you have ShopSite Pro, you could choose ShopSite's UPS option and add USPS via a module for the Custom Shipping Add-on sold by Lexiconn, see the add-on modules page at:
http://www.shopsite.com/partners-tools.html
Regarding the Handling Charges, you can enable the Handling Charge feature and instead of specifying a global formula you can add an individual handling charge to the Handling Charge field in each product's Edit Product Info menu (you will only see this field if you have the Handling Charge feature enabled).
-Loren