I've used many methods to pick colors and have found that most of them have drawbacks.
Like picking all the colors ahead of time and testing to see if they look good together can result in a great palette, but it can be tiring.
Using a pre-generated palette removes all the challenge of picking colors (and also the fun of picking colors). The generated palettes are often very limited in their range.This makes for a very cohesive page, but sometimes it feels monotonous.
Picking completely random colors can be hit or miss whether the colors actually look good together or not.
This random color wheel method I found removes some decision fatigue, but also usually ensures you can pick colors that look good together.
Step 1. (Optional)
Get a swatch chart that puts your colors in chromatic order. I use one similar to the one No-Sample222 posted in r/Ohuhu. Each page is a different color family. Each color is sorted into warm, nuetral, or cool. It then has groupings from light to dark in each category. You don't have to do this for this color picking method, but I find it makes it a lot easier
Even if you understand undertones and color theory, it helps to precategorize. Otherwise a color might fall into multiple categories. Like how do you decide if a color is a cool red or a warm purple when it falls somewhere in the middle?
Step 2. Make your color wheel
I used an app (Spin the Wheel). I added a section of the wheel for each color family in warm, nuetral, cool, light, dark, medium. For example for the orange color family I have these sections:
-light warm orange
-medium warm orange
-dark warm orange
-light nuetral orange
-medium nuetral orange
-dark nuetral orange
-light cool orange
-medium cool orange
-dark cool orange
Step 3. Pick a page
Step 4. Pick Colors
Next you simply spin the wheel and start coloring. I make it into a game. I can only spin and pick another color after I have used my selected color somewhere on the page. I keep spinning until I either have enough colors to finish, or I land on something that I can't find a use for on the page. When I use a color, I set it aside so I can use it again later.
The thing that make this so different from just picking random colors, is that you are picking a category instead.
So if the wheel lands on "light cool orange" I will have multiple options. I could pick a bright light orange for a pop of color, or I could pick something muted that reads more nuetral like sand or wood.
Because of this, it's hard to land on something that's going to ruin your page before you already have a lot of colors in your palette.
Step 5. Modifications
You might want to add a non random color at a certain point in the process.
Example 1: in the picture I posted here, every color is random except for the background. When I color, I usually save the background for last so I can pick something that ties everything together. I liked the muted teal color of the center fish, but I wanted the sky to be lighter than that. So I picked a lighter version of that color, and a yellow green marker to blend the sky into the sun. Similarly, for the sand, I wanted a lighter shade of another marker I had already used so I could have a good gradient from light to dark.
Example 2: for blending
On one page, I really wanted a metallic texture for some items. So I used a randomly generated color as a base, but I added in a lighter and darker marker so I could get a smooth blend.
Example 3: for shading
I'm my example picture I was able to do all my shading with my randomly generated markers. However sometimes it's fun to randomly generate your base and then add shading with darker markers after.