As far as transparent logos, the easiest way that I have found to create a transparent logo when I am unable to find one is by using gimp. There is a quick tutorial on youtube here:
https://www.youtube.com/watch?v=z_cv6MipiTw&t=165s
As is said in the video, the fewer the colors you are trying to remove the better, but it is by far the easiest method I have found and I have used this technique to create and then save the logos and other parts I needed as png files.
In terms of sizing and other aspects of actual disc printing, first I have to ask what printer and program you are using. A lot of members here either use Epson or Canon printers to accomplish this. Personally, I use a Canon. It comes with its own software for disc printing which I did not find to useful, mainly because I could not make circular text. I purchased Sure Thing Label maker and thus far I have been pretty happy, but you may find another program better suits your needs.
Here is an example of some minimalist disc art I am working on using Sure Thing:
