A good quality brush with long bristles. It can help some users if one trims the end bristles at an angle - say 30 degrees. Some brushes can be purchase cut like this.
Paint the ceiling first, then paint the deeper colour on the wall second (unless you have Goth tendencies and black ceilings)
I use a plasterer's skimmer to shield where you don't want to paint for doing jobs like that, also good for skirting boards if you don't take the carpets up.
I bought a triangular brush from Dulux ( part of paint pod set but sold separately) �4.99 on advice from v nice man in DIY shop. Didn't buy paint pod system however. I like the brush and as I have whole house to do will use it a lot.