Welcome to the boards!
Often books will have charts. You can do a simple search on "log cabin quilt yardage chart" that will show some examples that might lead you to a paid site/pattern that might be very much worth it to you. I typically make my own patterns with graph paper or using the Electric Quilt program. You can draw out your block (tape together multiple sheets if needed) and then measure the logs remembering to add 1/2" for the standard seam allowance no matter if your logs finish to 1" or 4" -- is always in quilting 1/4" seam allowance (1/2 for both sides). It is probably easiest to always use the short measurement for your across count, and make longer strips for the log length. For example, if you use a 2" (finished) log, then your cut logs will be 2.5" x some length. Using a 40" wof, you can get (16) cuts per strip. You need to remember both your "short" and "long" parts need to be cut. You then need to know how many blocks you will need -- divide that by 16 to find how many strips. Probably will be some form of a couple of full rows and a partial -- remember that you can use those partial rows for shorter pieces, unless you are using different fabrics for each row.
As a general rule, my queen sized quilts take roughly 10-12 yards, depends on the size of pieces and number of seams. Small triangles can have as much on the back of the quilt as the front! When buying fabric without a specific use in mind, I suggest 6 yards of things you love which is enough to make a focus fabric. I have a scrappy style and am cheap and typically buy 2 yard pieces and figure out how to deal with what I have.
With a log cabin, a lot depends on your log size and how many rows of logs in each block. Also, if your center square will be light/dark/different and what size it is. If you can provide those details we can probably make a better estimation, but I would say from what you've given us I would expect a pretty narrow log with 12 yards each (collected) light and dark -- but certainly not 12 yards per color! Can't help with the breakdown into 3 colors without more info!
There are many resources available to quilters -- don't forget your local library. As a beginner, I feel something like Eleanor Burn's quilt in a day book might be a good place to start. She also has videos. Many quilters have videos and blogs that may be able to help -- as well as us here on the boards!
https://www.quiltinaday.com/shoponline/book//216654