Sherry, I hate to burst your bubble but there are probably copywrite issues with you reproducing the Hospital's name and logo. Unless you spend more money for the machine you wouldn't have anyway to load the design.
the least expensive way to go might be to find out where the hospital gets the shirts and try to buy the logos from them as a sew on applique. I enquired at a stand in our mall where they will personalize items like hats and shirts for you with embroidery. They charge $.50 per letter if you provide the item.
Purchasing a machine is just the beginning expense. I have thousands of dollars tied up in stabilizers, thread, additional hoops and of course designs. If you want to download designs the machine has to either be USB accessable or you have to have a converter box like Magic Box. In addition, like everything else computer related the technology is constantly changing and becomeing out dated. The computer I am using right now won't recognize my "Magic Box". That is one reason I was forced to purchase a new embroidry machine that can transfer designs using a usb stick.