In my opinion, three software is the best for making Logo and Banner. 1. Photoshop. 2. Illustrator. 3. Corel Draw.
Photoshop/Adobe Illustrator - Apart from the cost, they takes a fair degree of learning and skill to use. GIMP +++ It is fast and easy to access. Plus there are loads of tutorials on YouTube, so you can virtually find everything you need to know. Also used some other online logo makers, like DesignEvo(https://www.designevo.com), which enables you make basic logos at once.
Illustrator is good for logo design as logo should be based on vector graphics and for the banner go with Photoshop as every should be based on raster graphics