If you want to design your own logo, which might be a bit of a learning curve but a good way to develop skills I can give you a few tips.. Good logos need to be:
1. Scalable - they should be created in such a way that they can scale up and down and remain clear (because of this professional logos are often done with vector graphics)
2. They should translate well to black and white - in instances where the logo can't be reproduced in full colour it should be able to retain its character and clarity in mono
3. Don't go overboard with too many colours, fonts, effects etc - look at all the biggest logos they're simple and clear, but memorable
Most pro logos are done in vector graphics software such as Adobe Illustrator - but there are free alternatives. Give Inkscape a try if you want to have a go making on yourself. It's not an easy process but it's a valuable skillset to have.