Here is some advise taken from Elizabeth Zimmermann's book Knitting Without Tears.
I have two tentative rules for you:
1. Be careful to use patterns that call for not more than five consecutive horizontal stitches of one color.
2. Avoid like the plague carrying more than two colors at once.
To depart from these admonishments is possible, but, to my mind, quite hazardous. It will add greatly to the difficulty of the project, especially for a beginner.
She says that she follows those rules strictly but they can be broken for a valid reason.
This pattern does pretty well on adhering to the rules. By rule #1 I think the basic idea is to use each color at least as often as to have only 5 other stitches between each use. For instance x00000x is all right whereas x000000x is slightly over the line. As long as your uses of the colors work like that I advise that you do not catch in the colors between uses but just let them float. And keep your floats nice and loose. If you don't the color panel will ripple.
This pattern falls within safe limits on that account. So that is good.
Rule #2 it breaks as it uses 3 colors, but only in 3 rows over the whole hat. So not too big a headache. A trick that will help in using a third color, like the center dot in the little flower like motif, is to cut the length of yarn you will need for that dot (be generous in your estimation so you make it around) off from the skein and then it will be much easier to deal with when it gets tangled into the works. You will just be able to pull it out or untangle the short piece much easier than if it had a big skein attached to it.
The question you asked about breaking the yarns... The pattern has pretty long breaks between uses of the colors in about every instance (if I'm remembering right). I prefer to break the colors and reintroduce them. Trying to carry them along somehow usually produces an unsatisfactory result in my experience.
I like to work over a tail of new yarn a couple of inches before I begin using it and then work over the tail of the color I just left after the color change. I find that usually works well and you don't have to work in a bunch of ends when you are finished. If the yarns are super contrasting sometimes that will show and then it is better to just begin working with the new color and work the ends into their own color.