Florence to Cinque.

The entire trail system is not open-- see this site https://www.incinqueterre.com/en/trails-advice

Take the train.

Study the trail situation to see where you want to base yourself. All the towns can be reached by train

Which one of the five villages should I make as a homebase in order
for me to hike up all the 5 villages ?

As Joe posted, it's not possible to hike all 5 by the lower coastal "Blue Trail" due to closures of two segments (Corniglia>Manarola and Manarola>Riomaggiore). There are other trails you can take to get around those but they're longer and more strenuous: not necessarily a problem if you're a conditioned hiker and don't mind the time.

There really isn't a "best" village - we all have our favorites - although Corniglia is the tiniest and takes a wee bit more effort to get to/from. You need to either make a steep climb from the train station there or take a little bus which zips up and down the hill. Personally, I might look at either Monterosso or Riomaggiore? You could, say, hike Monterosso>Vernazza> Corniglia on the "Blue", take trains to Manarola and Riomaggiore, and then ferry back to Monterosso. Or do that same trip in reverse.

One thing, though? If your trip is THIS SUMMER, you're very late in the game for finding accommodations in the CT: they book up pretty quickly and far in advance of high season. You may need to take whatever is still open in any of the 5, or look in Levanto or La Spezia if what's still available doesn't suit. I'd look into making your reservations ASAP.

Definitely take trains from Firenze.

First of all if you don't say the full name (Cinque Terre) Italians won't understand and will think you want to go somewhere at 5 o'clock (Cinque means 5).

Using the www.trenitalia.com website enter:
from FIRENZE (tutte le stazioni)
to name of village of choice

Note that there is a high speed FrecciaBianca going there at about 7:30am. from Firenze Campo di Marte station. It's the fastest and the only FB to La Spezia from Florence, if you don't mind the early departure.

Any village works, they are just minutes apart by train. I prefer Monterosso. More amenities, better beach, not as crowded as Vernazza. Vernazza is the most visited.