Versatile Symbol Logo Design

I need a fresh logo built around a distinctive symbol that can live comfortably on its own or lock-up with my company name. The primary stage for this mark will be digital—website headers, profile avatars, posts, and ads—so it has to read crisply at both thumbnail and full-width banner sizes... (Budget: £10 - £20 GBP, Jobs: Adobe Illustrator, Adobe Photoshop, Banner Design, Branding, Graphic Design, Logo Design, Photoshop, Vector Design)