I have always used wither PowerPoint of Microsoft Publisher to create logos. The files can be saved in many different formats and sizes. I would suggest creating one on your own. Allowing a company to create it could give them rights to the logo (or at least partial rights if you are not careful).
Do a little research on-line to check logos similar to the one you are looking to create. This will help getting you started. After that, start playing around with image creations on the software you choose to work with. I have always had a lot of fun designing my own things. Gives you ownership, pride, and the satisfaction of seeing something through to the end.
Actually, there are several ways to create a logo using most common computer software. The hardest part is the idea. I suggest drawing or sketching something freehand first. You'll need to try several designs. Keeping it simple is the key. A program like Microsoft Publisher would be useful for creating the actual logo.
Creating a personal logo sounds like a great job for Adobe Illustrator, which allows a person to draw their own designs on-screen or combine them with text, graphics or other downloaded images.