It's actually quite hard to make a transparent logo starting from a JPEG, because the first thing you have to do is try to select and knock out the background. It's almost easier to create a blank document with a transparent background and start pasting or writing things on top of it.
On lower quality JPEGs, the background may appear white or black, but because of a compression effect called "mosquito noise", that background is probably hundreds of different off-white colors. When you start trying to select these colors, you end up destroying parts of the actual image.
Alternately, you can manually go around with the lasso select tool and laboriously select all of the white, black, or other background color, and then delete it. I've spent hours doing this on elaborate, high resolution JPEGs before.
I'm glad you're having fun putting logos. It's easy to get wrapped in in the labor of getting it "perfect" but I realize most people will not do that.