So basically from what you have described, all you need is a modern Core i5 CPU and a SSD.
Modern Core i5 CPUs come with either 2 or 4 cores. A dual core i5-7200u should be fine for your needs, a quad core i5-8250u would be better if you do a lot of multitasking, but generally speaking for average daily tasks you should not notice much of a difference. However, a laptop with an i5-8250u CPU will likely exceed your budget limit.
If you "can't stand waiting for everything to load up all the time", then you are better off with a SSD (solid state drive) since they have much higher read and write speeds compared of a HDD (hard disc driver or simply hard drive). SSDs cost more so laptops with SSDs typically have 128GB or 256GB capacity. A...