Existing Logo Refresh Needed

You can download my current logo here: https://limewire.com/d/iukLY#fl0wJclMso. I want to keep the identity people already recognise but give it a sharper, more contemporary feel that works just as well on a phone screen as it does on printed material... (Budget: $250 - $750 USD, Jobs: Adobe Illustrator, Branding, Graphic Design, Illustrator, Logo Design, Photoshop, Typography, Vector Design)