I want to know what kind of effect a large circular space station would have on the planet if it went completely around the equator in one giant circle? Would it impact gravity or anything? And would the planet have any effect on the space station?
A ring is not stable, so it would require an attitude control system for stationkeeping (this was the problem discovered by MIT students concerning Larry Niven's Ringworld (source)).
It would not have any significant effect on the planet, except they would see a light ribbon in the sky if the station is large and near enough.
There are serious stability issues as addressed in other answers.
The solution though is to tether the ring. You build a number of space elevators along the equator, and you attach the ring to those space elevators.
The tension in the cables keeps the ring in place and you now have an excellent launching point and can even use it for travel around the planet.
Note that we are not yet able to build space elevators, but we're getting closer all the time.
The space station would have virtually no effect on the planet beyond possibly being visible as a line in the sky. It just doesn't have enough mass.
The principle of an orbit is that one object orbits another. Each could be considered a particle at its centre of mass for the sake of defining its location.
The centre of mass of a planet is in its core, the centre of mass of a satellite is harder to calculate but it's somewhere in the middle of the object itself. The centre of mass of a ring is in its centre.
In your case the centre of the ring is in the centre of planet, there's no orbit. Each object, planet and ring satellite, has no gravitational effect on the other.
This is covered by Shell Theorem, but the short version is, your full ring space station is not practically possible.