What sort of budget are you looking at, your budget is the main factor in what you should be looking to spend your money on.
Personally I would treat an SSD as an absolute requirement for this, you're going to likely want a machine that will be good for things other than video editing and running a laptop with a hard drive nowadays will make the whole thing feel sluggish in daily tasks. You do have lower capacity however GoPro footage isn't huge and you can always use an external hard drive to archive footage when you aren't working on it then edit off of the SSD for good scrubbing/rendering performance (especially when working with 4k). In the past I edited off of a hard drive and it became the thing that bottlenecked rendering performance and made certain actions like scrubbing or generating audio waveforms frustratingly slow. If your budget allows, go for one with "NVMe" or "PCIe" SSD storage rather than a "SATA" SSD, you pay a bit more but it's several times faster. I'd basically ignore anything around SSDs "wearing out" - they technically do but having properly stressed cheap SSDs by capturing uncompressed 1080p video to them with them still going strong and also having SSDs from 2011 still going strong, I wouldn't be worried, by the time it would take you to wear out the drive, you'll have already probably upgraded to a newer machine.
CPU wise, I'd stick with Intel as their QuickSync video engine will massively improve video rendering performance. For context, I used to render my videos using my 8 core AMD Ryzen 1700x desktop which rendered at around 80-90fps. On my Quad Core i7 MacBook Pro with QuickSync I can render at 150fps easily. You probably also want to go for something quad core or greater and bear in mind that the CPU models ending in "U" are lower power consumption models which aren't as powerful.
For RAM I'd see 8gb as a bare minimum, 16gb would be even better if your budget allows.
Also look at the screen resolution, I'd go with something at least 1080p, something cheap like 1366x768 will feel very cramped. An IPS panel will also be good to get decent colour accuracy when working with video.
Outside of that, you'd also want to keep an eye on things like build quality, battery life and portability. You could probably get a machine with insane specs for a really low price but if it weighs a tonne, falls apart when you slightly bump it and lasts 45mins on battery, it's probably not the ideal option!