The rule to keep in mind is that you should never wear the same pair of leather shoes 2 days in a row (it's bad for the shoes.) So ...
You need two pair of dress shoes. One pair black and one pair brown or tan (depending on your suit colour preference.) You would need a third pair if
a) you want to always wear brown shoes and save black for weddings, funerals &c. or ...
b) you want/need to wear black shoes for work at least part of the time (eg lawyer) so potentially two days in a row.
If both 'a' and 'b' apply then you need 2 pair of black and 2 pair of brown dress shoes. Style of those shoes is debatable and depends on personal preference, except you should have one pair of black captoe lace-up oxfords for formal occasions.
Casual shoes ...
There's a lot more room for variation here. We can be talking anything from retro canvas sneakers to tough guy biker boots to Doc Martens to ... well, there is almost no end in sight.
You need a decent pair to be seen out and about shopping or hanging with buddies and whatever. If you are getting leather shoes, get two pair for the reason stated above.
You need a pair for doing the grimy chores &c. that you don't want to get your good shoes dirty doing.
You need a 'good' pair for stepping your game up, taking ladies out on dates, going to Church, or whenever you are doing something "dressy casual." If you picked the right models, one or more of your dress shoes can do double duty here if needed.
