Very common materials for each I have found to be:
Shooting Patch Material:
Walmart Blue Pillow ticking. Sewing section at Walmart, sold by the yard. (about $6/yd)
Looks like this:
https://www.onlinefabricstore.net/4...yGfPV2nLyA9RKAAPKzDp1d0LfCYrJkkhoCYZ0QAvD_BwE
Cleaning Patch Material
Walmart 100% cotton muslin
https://www.walmart.com/ip/Waverly-Inspirations-100-Cotton-Natural-Muslin-Fabric/49332641
Or you can have it cut by the yard.
Some people get from Walmart, some get from Joann fabrics, some get from other fabric stores. Whatever is convenient.
For both patch lube and cleaning solvent, things really start to diverge there.
Lots of people have various formulas. Many (like I) spit patch the Shooting patch and dab on some MAP onto the cleaning patch.
MAP is equal parts of Murphy Oil Soap, Rubbing Alcohol and Hydrogen Peroxide.
Again, see a shooting line of 20 BP shooters and I'd be surprised if 2 people did the exact same everything.
Oh, then there is cutting at the muzzle, vs pre cut shooting patch.
round vs square cut cleaning patch.
to answer your question about 1" vs 2" cleaning patches, 1" cleaning patch would have to be a really small caliber gun like a 32. (not sure about 36).
If you are talking a shooting patch, if you are buying them, it should say the caliber it is designed for. I think my 40cal I made 1" or 1.25" round shooting patches.