Frag is short for fragment. It is when you cut off a part of a coral to start a new one.
I wouldn't really recommend a small tank for beginners, mainly because of water chemistry. In larger bodies of water a small problem is easier to correct and less likely to kill off animals. In a small tank, there is not much room for error. I also have a 150 gal DT and 20 yrs experience. Not saying it can't be done if you research like crazy, and go slow.
We are here to help if decide to try it, but i recommend you go with the largest tank you can.