also if i am doing this should i make my core cities further apart so that they can grow more and become more productive
Until you get hospitals, cities can't grow past size 12. And hospitals come late in the game, when the game is already set up for victory or loss.
So place core cities such that they can work 12 tiles, but close enough that no tiles go un-worked by any citizen. This is more easy to do in conquest, because in vanilla and PTW, the ring placement interferes.
The specialist farms, it is wasteful to build anything in it that cost upkeep, so don't, don't even build aquaducts. Many of these cities won't grow past size 6, and even then, they don't need to have more than 4 citizens working the land for food. (even less, often) So place as many of them as you possibly can on the map. So that you get the small benefit they give as much as possible.
If your game is going to last until the modern age (space race?), and you want to make an empire of big metropolises, then maybe grow a metropolis area next to the early core, and swap the capital. So you can have a small efficient core in the early turns AND a big efficient core in the later turns.
Or use a special ring-pattern with temporary cities that can be abandoned later to make room for other cities the grow.