this will be a patchy blanket, indeed.
You can not really make it look nice with extreme differences (bulky and chunky combined with sock yarn, but you could use very thin yarn double stranded), I guess. But differences will just add to the style.
make a swatch with every yarn (or make your squares so small that you do not mind to rip out). The swatch should be bigger than 4 inches wide. Then measure how many stitches you have in 4 inches and calculate how many stitches you will need for your desired size of patch.
The number of rows does not matter as much since you can just keep knitting until the length is reached.
The needle size mostly depends on how lose or tight you want the stitches to be. Just try it out. There is no wrong size, there is just too lose, to tight, and so on. It will not matter extensively, so do not over worry. You will see on your swatch if the stitches look good (the rows a bit underneath the needle, not right under it, since sometimes they look different.)