Once you've established how much RAM you think you need — and then doubled it — the CPU (processor) should be the next spec you look at.
Many of the computers you'll be looking at will come with CPUs from Intel, and they generally come in more-or-less easily discernible performance packages. The Core i3 line is a relatively low-powered line of CPU. The Core i5 is mid-range, and the Core i7 is top of the line. Some computers have ultra-powerful Core i9 models, but people who buy those computers already know what they're looking for.
With Intel's latest 8th generation of CPUs, almost all of its models have at least four cores, including the low-power Core i3 models. Higher-end models have six or more cores. The more cores a CPU has, the faster it can open and run several apps at the same time. With that in mind, a Core i3 will actually suit a lot of people for basic tasks, more so than previous generations of Core i3 CPUs that only had two cores.
The reason why you'd want a mid-range Core i5 or high-end Core i7 is if you want to open and run many apps at the same time even faster.
As it is with RAM, casual users who don't really use computers that often will be fine with Core i3 CPUs. But those who use computers a lot will want to look at the Core i5 at least, and potentially Core i7 models.
Personally, I don't buy a computer with anything less than a Core i7. I want apps to open quickly when I need them, and I want them to do the things they do as fast as possible for my work. For example, I benefit from using a Core i7 when I run Photoshop to bring you some of the pretty photos of products I write about. I have no time to waste for things to load and render while editing and saving photos. And as for web browser tabs, I have no time to wait for slow tab switching while researching for a story.
Some computers come with AMD's line of Ryzen processors. I don't have much experience with AMD's processors, so I can't accurately say which one will work for what type of user you are.