The answer is for the freshest coffee you must
grind your own. Assuming that you can obtain reasonably freshly roasted beans from a specialty store, there is no question that you will notice a profound difference between
pre-ground beans (which are likely stale, as
ground beans are fresh for about 15 minutes and then start going stale), and freshly
ground, freshly roasted (two weeks or less) beans.
About the
grinder. First is MUST be a
BURR grinder...not one of those chopper things which will destroy the best of beans. As far as expense goes...if the
grinder is to be used for drip or press, an inexpensive
grinder will suffice. However,
grinding for pour-over or espresso you need a better
grinder. I don't mean to dip into your pocket

p), but spend as much as you can reasonably afford for a
grinder. Aside from the beans, which are clearly the most important element in an coffee production (the most expensive machine and
grinder can't fix bad beans...GIGO!), the
grinder is the next most important element in an espresso set up. (After that...good dosing, tamping and extraction timing are the next most important elements, and finally the espresso machine...at the bottom of the list).
You might want to take a look at the
Espresso Enthusiast thread...there are many knowledgable folks there who just love to talk coffee, and also love offering advice, suggestions (about technique and equipment) to anyone who posts there. It is a very welcoming and friendly...if slightly insane thread inhabited by total coffee crazies!
You might want to discuss your current espresso set up so we can see where you are going.
BEWARE: we will spend your money freely...so keep a tight grip on your wallet!
About a moka pot. You say that you have an espresso machine. While there are many who love a Moka pot, and with GOOD BEANS, and a GOOD
GRINDER, and proper technique, you can make wonderful coffee with it...it does not make espresso. No reason not to have both...and espresso machine and a moka pot for variety sake.