I've uploaded some images of my sketches. These are my ideas and may help but please don't feel that you have to stick to them. I'm sure you're a lot more creative than I am.
The logo is mainly going to be used as the header for our website. While I want people to see the logo, I'm more concerned about them seeing as much content as possible when the page first loads so the shorter (height) the logo the better. Short and wide is the way forward!
It will also have to be on a white background as it will be a white background on the website so please make all submissions accordingly.
Last but not least, just because some of my sketches have "Est. 2015" and an axe in them, it doesn't mean I expect them to be in all submissions. Perhaps just an awesome typography is enough to pull it off. The only thing I definitely want in there is the words PALEO PAPEO.
Please ... play around and see what you think works for our brand. You are the designer and I'm sure you can come up with much better ideas than I can.
This is for a Spanish store but here's a UK store that is similar to ours so you can get an idea of what it will look like:
PS. Please ignore the sketch of the pig :-D