Getting a case is a good idea. I'd suggest something in simple rubberised plastic is you are not too concerned with the aesthetics of the phone after the cover. It won't have a long life but should be cheaper, even if you consider replacing it every 8-9 months or so. Vendor to check out for these: Casetify or your local mobile shop.
I would not advice going with the PU leather as those are highly unreliable with regular usage. Even with great quality stitching, the outer layer can easily come off in about 7-8 months. It's just better to spend a little more and go for actual leather in that case. You won't find many vendors offering leather cases for Motorola Phones. I saw some on Noreve, but not sure if they carry case for the G6. Please feel free to check.
Also, don't do the thing where people go with the dimensions of the phone and get the case. It does not work out in majority of the cases. You may very well end up with incorrect placements for the buttons, wrong camera/fingerprint/earphone slots. It's better to look for 10 more minutes and find a reputable vendor that provides quality goods.