Chinqua Terra

The best town in the Cinque Terre to stay in is the one that appeals to you most. Have you read about them? Im not intending to be rude, but they are different and rather than write a description, Im sure you could find one. Some people like Monterosso del mare (the northernmost) because it is largest and has a beach. Some like Vernazza (next one south) because it is famously photographed. Not as many people seem to favor Corniglia because it is not directly on the water. I stayed in Monterosso on our trip and would probably stay in Manarola the next time. Truly, take a look online.
As for the trail, there are different sections. I dont know how long it takes to hike all of them in a day. We hiked from Monterosso to Vernazza, ate lunch there, hiked on to Corniglia, and took the train back to Monterosso. The next day we took the train to Riomaggiore (farthest south of the 5) and hiked over the hill north to Manarola, and took the train from there to Monterosso (so we never hiked between Manarola and Corniglia). Each section takes the time it takes depending on how fast you want to hike it. I think each section took 90 minutes for us but I cant remember (and we did it with three kids). I think Id hike it faster without the kids. The hike from Riomaggiore over the hill to Manarola was steep. Again, not know ing anything about you, ymmv

CINQUE TERRE
( important to use correct spelling when researching foreign destinations)

Here is a start
https://www.ricksteves.com/europe/italy/cinque-terre

https://www.cinqueterre.eu.com/en/footpaths-cinqueterre

How fast you can go is dependent on your level of fitness and 'traffic' conditions

.... and hike the path between the towns

There are many trails in the CT but the "path" I think you're referencing isn't open between all five villages, and hasn't been for quite a few years now. It's called the Sentiero Azzurro (Blue Path) and is closed between Corniglia and Manarola, and Manarola and Riomaggiore. The only two sections you can hike are between Monterosso and Vernazza, and Vernazza and Corniglia. While there are other trails between Corniglia ,Manarola and Riomaggiore, they are longer and more strenuous.

There is a map and a lot of good info on the website for the park (the Cinque Terre region is a national park):

http://www.parconazionale5terre.it/Eindex.php

The website can be a little slow so be patient with it. :O)
"Best" town is up to personal preference but we enjoyed Monterosso as it's the largest and so is able to distribute large crowds of tourists more comfortably than the smaller villages.

Regarding the first part of your question, "how long" will depend on how much you want to see there and how much activity you want each day. For many people, three nights / two full days allows a hike of the trails and a brief look at all five towns. If you want to use that area as a "base" to explore other parts of that area, then add a few nights. It's a great place to take a few days to recuperate from strenuous travels in other parts of Europe.

The "best town" is pretty much a matter of personal preference. I agree with the previous post and also prefer Monterosso as it's the largest of the five towns, and has the most tourist amenities such as hotels, restaurants, shops, etc. as well as the largest train station and the best beaches. Parts of the beaches are "pay-per-use" but there are free parts too. The hotel staff can point out which parts are free.

The smaller towns tend to have B&B / Affitacamera accommodations, sometimes with many stairs and sometimes no breakfast is provided. Monterosso has larger hotels with facilities like elevators and many provide breakfast in the cost of the room.

Before the pandemic, the Cinque Terre was dreadfully crowded at times due to cruise ship groups and also bus groups from other parts of Europe. That tends to be a problem mostly in the daytime and the evenings are more relaxed with fewer crowds. I don't know how quickly the crowds will return now that restrictions are being loosened, but it probably won't happen right away.

As I usually suggest, use the RS Italy guidebook to plan touring, accommodations, etc.