Beginner: is army painter fanatic starter set good for me or should I get something else?

Hey all!

Some quick background: I have no painting experience at all, but am looking into getting into painting for the dungeon and dragons games I DM.

I have no paints or brushes, but I do already have a big batch of miniatures (Dungeons and Lasers Deuslair core pledge) to practice on. I also got a wet palette recently.

I was looking into getting the Army Painter fanatic starter set (https://thearmypainter.com/products/warpaints-fanatic-starter-set?srsltid=AfmBOop4L-iVPONUx_6P0LnVikcEMtvMXaRSMxRWi_6F-8DQapBl6AzD) since it comes with a brush, paints and how to paint booklet, but I feel like the paints included are mainly aimed at the miniature in the set and lack flexibility (no skin colors for example). Is this true? Also, an important question for me, how good is the beginner guide included in this?

If so, which set should a beginner get to get started and have a selection of paints for a wide variety of figures? I am mainly looking into sets since I have no idea what I'm doing, so having all colors selected for me greatly reduced the barrier of entry.

Thanks in advance!