I've read it makes a big difference, although I'm not sure I believe it.
It does, imo. The taste using pre-ground beans is ...flatter? Not sure how to describe it, but I do taste a difference.
I got this Cuisinart Supreme Grind Automatic Burr Mill last year:
...because I'd read that having a uniform grind also makes a significant difference, and this particular grinder had a good rating for that. I don't personally notice much difference in taste as a result of uniform grind, but I'm still glad I got the grinder because I can determine the size of the grind with a setting (instead of simply grinding it until it looked right) *and* I just push a button and it automatically grinds a determined amount each morning. It's kinda a pain to clean every week or so, but much easier than cleaning smaller grinders more often. It comes apart easily and half of it can be put in a dishwashing machine.
I also find the uniform grind handy when making cold brew because smaller grinds can really clog up a filter.
As for brewers, I use a standard Mr. Coffee drip brewer. If I'm drinking the coffee hot, then I like hot brew more than cold brew because it has more of a kick.
For cold brew I have the Toddy cold-brewer. I dabbled in jerry-rigging a homemade brewer, but it's a pain in the ass to drain. This brewer makes it super easy.
I like cold brew for when I'm actually drinking the coffee cold. I'm not a big fan of using cold brew for hot coffee though. (Or it's possible I just haven't figured out how to do it right). One benefit of cold brew is that it's a lot smoother.
Another upside of brewing cold is that it's a lot less acidic. I have some problems with heartburn, and I expect I'll probably need to go mostly cold brew at some point in the future.