It definitely makes sense to do the Causeway Coastal Route one way and go inland the other. I prefer the route going via Carrickfergus on the way there and then returning inland but this does mean that you would be better doing the Causeway later in the day to avoid tour groups.
Best time - probably either first thing in the morning or in the evening. On a good day, you will have visitors no matter what time of day but tour groups tend to arrive late morning/lunchtime.
Some people believe the best time is at low tide - this probably is mainly for photographers so it depends if you are a point and shoot person or interested in more atmospheric, skillful photos.
There are previous threads on this forum re tide times e.g. this one
tripadvisor.co.uk/ShowTopic-g186591-i88-k439…
I would allow 1.5-2 hours at the Causeway but if it is raining or windy, you can just get the minibus both ways, take a few photos and do it in less. On a good day, enjoy it and give it the time it deserves, look for the shapes (boot, organ etc).
Don't forget there are lots of possible attractions along this route e.g. Carrickfergus Castle itself, Waterfall walk at Glenariff forest park, Carrick-a-Rede rope bridge, Bushmills Distillery, little villages, lovely beach walks, Dunluce Castle (not just a photo shop, great views from here and very good AV show), a photo stop at Downhill for the views of Mussenden......
Edited: 09 February 2012, 18:26