So what you’re looking for is a “color palette” that works well. Since your logo is a dominant part of your branding, it’s often times good to start with the colors you like for your logo and build the site around those colors.
One thing I like to do is start by looking at how other people do it. Canva’s blog has a sampling of color palettes for websites. That post takes it a bit further by describing the mood and even links to the websites so that you can see it yourself. The point is to just look at what inspires you, not necessarily read through everything (I still haven’t, and I’ve had it bookmarked for a minute now)
You want to try and make sure to look for palettes that work well for websites, since a lot of palettes look really good but don’t necessarily make sense for reading etc. These are color palettes you might not necessarily use for a website, but would work well together for things like logos.
Finally, in general you can make use of a color wheel to see which colors work well together. Adobe has a nice interactive color wheel for web developers, allowing you to set the number and range of colors you want to use and even has options to show you how people of different color blindness levels would perceive your palette: https://color.adobe.com/