FONT: I do not have any specific font in mind. I want something easy to read but I do not want it to look like it was typed in word pad with basic fonts. I want it to look professional. 
 
STYLE: I am not looking for any specific style so to speak. I will know it when I see it though. I want something classy and professional, I do not want something gaudy. 
 
This logo will be used on tshirts, business cards, letter heads, signs, and even outfits/scrubs that the workers will be wearing. Knowing this I want a logo that has the ability to be a web logo and and offline logo. 
 
You can use gradients at your own discretion although I am not a big fan of gradients, so if I was to use gradients any where in this logo it would be on the stethoscope, but that is not required and I might not even like it. Use your best judgement as a designer. 
 
WHAT I AM IMAGINING FOR THE LOGO: This is what I see when I picture the logo. I want the logo to be bright and attention grabbing yet I do not want it gaudy. Simple and Stylish Text would be great, and then I am leaning toward a illustration. I am think a very cool play on words and equipment here would be to have a Traditional Doctors Stethoscope in the logo somehow, with one minor twist...instead of the Chest Piece on the end, I think it would be very cool to have a iPhone lightning cable end on the end of it. See the attached picture for references.

Phone Doctors of South Georgia LLC.