I personally look for the specs so sometimes they may have a good deal on a specific server type rather than just a flat % or $ discount. Obviously any sort of discount is great, but for me nowadays it's more about the other types of services. DigitalOcean (DO) does a great deal where they'll give you credits to use on your account for a few months so you can basically get a powerful VPS or Dedi free for first few months which drops the average cost of the server lower than some competitors. However, I use DO for many more reasons than cost - they are not the cheapest but I've found them to be very reliable, easy to manage, and their backend API is cool because you can clone servers, start/stop servers, etc.
In general, if anyone is wanting to start their first server I suggest looking for a minimum of 4xCPU (or if a small or brand new project then maybe a 2 vCPU vps), ideally 6-8GB of RAM (again, if a small site then 2-4GB is fine), and I would usually suggest going for something that has SSD storage because it's just faster than traditional HDs. From there it just becomes how fast their internal & external networking is for the port - try to go for a 1Gbps if you can.
I take a look at what the service offers before looking at the price. If the hosting has what I need and it has a deal, that's just a plus for me! Though you might need to be weary of some companies. If it sounds to good to be true, then I would make a quick google search of reviews before going with the company.