Mini-DVD-R exist (use -R, not +R). But the Cube is not actually good at reading burned discs. It may require opening the console and adjusting the potentiometer (lowering the resistance) for the laser. You may have to try multiple types of blank media. Ritek G04/G05 are considered the best, but hard to find nowadays.

In order to use burned discs or software from SDs you need the possibility to start Swiss. If you own one legit disc from the list here:
http://www.gc-forever.com/wiki/index.php?title=Booting_Homebrew (this wiki is a good starting point for many GameCube questions)
You can use a save exploit (else just buy the cheapest game). The boot.gci from the Swiss package does not fit on the “Memory Card 59”

The only problem is to get the save exploit on the memory card. Easiest way is using a hacked Wii and software like GCMM.

Once Swiss is started you can

• (try) booting burned media
• load ISO files from SDgecko (passive adapter; very cheap)
• Start homebrew software like GBI from SDgecko (and you can even boot GBI from normal memory card without Swiss)

 

please use this, its way better and no lag like the official one https://www.gc-forever.com/wiki/index.php?title=Game_Boy_Interface

 

also to boot gbi you can use this: which would be cheaper than the official gb player disc https://www.codejunkies.com/Products/SD-Media-Launcher__EF000580V.aspx