If you have no design/graphic skills currently, there's no better way to learn than a practical project :-)
You mention wanting to stand out on itch.io, so the first thing I would suggest is finding what your neighbors art looks like. Whatever categories you might fit into and find yourself competing with, scour through them. If everyone is doing detailed, Swords&Sorcery style cover art, do something simple. If everyone is using a multitude of colour, opt for something with a minimal palette. I think you can see where I'm going with this.
For the logo itself, try to really figure out what you are looking for style wise. Look at other logos to try and find the feel you want. Go to https://dribbble.com/ and search for "style of game + logo" and most likely there will be stuff to see for inspiration. Then start drawing those logos yourself by hand on a piece of paper, and doing variations of them once you get comfortable. Don't worry too much about details, just get the basic shapes right. Just get used to drawing these sorts of objects.
Then, just jump into drawing your logo. Take your ideas and distill them down as much as possible. Feel free to explore, and do as many variations as you can. Do it until you never want to draw another logo again.
Then from the mountain of them all, look through and start taking notes of the ones you like. Make note of what it is you like about them, and try to figure out specifics. Make notes of ones you don't like, why you don't like them, what you might be able to change so they were better.
Then, take all your notes and re-draw all those logos a few more times, tightening up the design, and see which ones are starting to stand out more now that you have refined them a little.
When you've got something you think you can work with, take one of the free software options out there and start learning how to convert your drawing into a digital file with your chosen software.
If along the way you need some help, let me know. It'd be hard to teach you everything about logo design in the remaining time, but I'm willing to help out as much as I can. :-)
P.S. Another art-asset option worth looking through, all sort of different packs available. https://www.kenney.nl/