There are multitudes of ways to watch online videos nowadays, and a laptop would not be top of my list. Unfortunately, the “best machine” will depend on your personal needs and preferences. In fact, many people use more than one machine, and your best option might be a laptop plus a cheap streaming device.
£600 doesn't really buy you a huge amount these days. A mid-range laptop or maybe a reasonably high-end smartphone. Or, alternatively, you could buy a 50" 4K HDR TV perhaps.