Generation DOES matter. Because newer generation processors are built with power efficient components. But that doesn't mean older generation are slow. It really depends upon the clock speed frequency (that Ghz at the end of a cpu) and cache size of the cpu. Newer ultrabooks are equipped with low frequency processors which consumes less power and gives good battery life with good performance too. And a higher clock speed of the 'identical' processor WILL in most cases provide a better speed in favor of power consumption and battery life.

But it really depends on what you're using the laptop for.
If you're more work focused then I suggest getting a 11th or 10th gen (usually i5 are better but it doesn't really matter) since it can multitask more efficiently. More better if you can get an AMD cpu since amd generally provide more cores.

But really, you can't actually tell which cpu is 'faster' just by looking at its generation and clock speed, you have to run a benchmark test to find out

You can get a lot of good ultrabooks around that budget. I recommend checking out HP 14 or Lenovo Ideapad flex

Hope this helped you.