WARNING: VERY HABIT FORMING! For some it comes on gradually and other it hits instantly and you find yourself looking at what tools you can sell to be able to by more pen turning tools and upgrades!
Welcome. I started with a very mini lathe called the Taig. I was living overseas and it was the only thing I could put in my suitcase. Then when I was back in the USA a year later, I upgraded and had a larger lathe and paid to have it shipped back overseas with me.
Before investing in many tools, use the lathe you have and do some research as to what tools are needed - just as you are now for a mandrel to fit your particular lathe. For me on my Taig, there were some options but not a lot, and I suspect the same for your lathe. The MAIN thing to look for in an upgrade, if that is what you decide in the future - look for a lathe with an MT2 morse Taper. MT2 is the one standard that offers many many options.
For your lathe, and I looked it up and it looks like the tail stock has a live center that is made for turning wood. When using a mandrel, the mandrels are made of metal of course, but metal mandrels require a 60Ā° live center in the tail stock. The one currently in the CWL 1000B appears to NOT be the 60Ā° center. What that will do is cause the very tip to ball up or bend just a tad, and that will result in eccentric turning. See if you can find a 60Ā° live center for the tail stock.