Which Village of Cinque Terre is best to start the trail?

I would suggest to start in Monterosso. The stretch from Monterosso to Vernazza is one of the most beautiful and also a more strenuous one. It's easier to do early in the morning when you are still fresh and the temperatures not too high, yet.

Diana,

While that's somewhat a matter of opinion, I agree with Beatrix that it's best to start early and while it's still relatively cool. It's also the best choice as you're staying in Levanto, which is only about a four minute train ride from Monterosso. The beginning of the trail is at the far end of the "old town" just above Hotel Porto Roca, which will be about a 10-15 minute walk from the station. Note that you'll require a Park Pass to hike the Sentiero Azzurro trails, which you can buy at the beginning of the trail. Be sure to take lots of water.

The Monterosso to Vernazza section is the most challenging, as there's a considerable climb at the Monterosso end. Once at the level of the trail, it's mostly an easy stroll although there are some narrow parts. The Vernazza to Corniglia section is not quite as strenuous, but it will still take a bit of effort.

The trails from Corniglia to Manarola and Manarola to Riomaggiore (Via dell' Amore) are closed until next year due to damage. Therefore, once you reach Corniglia you'll have to walk down the long stairway to the station and take the train from there to Manarola, and from Manarola to Riomaggiore. The train trips are all very short. If you buy the Cinque Terre Treno card, that provides not only the pass for hiking, but also transport on the Regionale trains in that area and I believe also back to Levanto. As I recall, it also provides passage on the small Shuttle Van that goes from Corniglia to the station, which will save you a hike down the stairs.

Once you reach Riomaggiore, you might consider taking the boat back to Monterosso as that provides a nice view of the five towns from the water. Note that the boats are "weather permitting", so if the water is too rough you'll have to use the train. If you need directions to the boat area, post another note. Once you arrive in Monterosso, you could stop for a fine dinner in one of the excellent restaurants there, before returning to Levanto by train. You might try Cantina di Miky, which is very close to the train station.

Wow!
Thank you so much for your advice Beatrix :) And Thank you so so much for your perfectly detailed advice Ken.
I'll surely print this one out. I'll be traveling end of Sep, 2014 :) Sadly, to hear that the road of love is closed .. oh well..

Thank you,
Diana