If you are launching from the equator (and are launching in the middle of ocean) then you can chose the inclination of your launch (therefore have a larger launch window if your destination is the moon). But you will get the most velocity added to your rocket if you launch into a 0 inclination.
If your space station is at Earth/moon L1: Any launch inclination can reach it and you won't need to pay (in delta v) in order to reach it from that particular launch location (though you still lose from not launching from equator at a 0 inclination- which uses the highest percent of the planetary spin). If you launch directly to L1 and your ultimate destination is the Moon, Mars, or anywhere beyond Earth, then you will pay less in terms of delta-v then compared to going the LEO (the energy needed to circularize a LEO orbit is wasted delta-v if you are going beyond LEO- added to this, the delta-v needed to reboost to counteract atmospheric drag [which becomes quite significant if your space station is in low orbit for months or longer]). One main advantage of LEO is you can get the largest payload from a rocket to this location. If a rocket can lift 24 tons to LEO then if can only lift about 12 ton to L1. So if you need a single piece which weigh 24 tons you would need to first go to LEO then dock with another booster lifted by same rocket in order to get this large chunk to L1. Or use tugs, or use a gas station [and tugs].
One advantage of launching from equator at 0 inclination is you have a launch window every 90 mins in order to launch a second booster to lift your primary payload to higher orbit.
Another thing is that if everyone launched everything from equator and at 0 inclination you wouldn't as much of a problem with manmade space debris- a screwdriver lost in a 0 inclination LEO orbit will never have much velocity to other things in a 0 inclination LEO orbit. Of course there is already debris in orbit and high inclination orbits are useful for many purposes. Btw might be a way of getting rid of debris- all orbits will pass through (cross) a 0 inclination orbit. So if you could "put a gas ring" at 0 inclination this could cause drag to all objects passing through it- of course that includes satellites AND that's a lot of gas:).