a hell rofl... just kidding back to the topic...

it depend on how good are you with the Nagato and how well you play it + the event right now it will be fast to get to Yamato

Frankly, I was never a huge fan of the Nagato for whatever reason. But, IJN has the Fuso, which is one of the best BB2s, holds the same crew, and (when using 14") has more spare displacement before losing that all-important knot. As a result, if you don't like the Nagato but play the Fuso well, you can use that all the way up. Or you can mix it up between the two.

Depends how you good you are at with nagato, like erwinja said, fuso might be good choice for you if you don't like nagato. Still there is always IJN PBB. It's a mini version of yamato but lower range and firepower of course. But it is still overpower if you have high level crew stand by already. 

Loved the Nagato myself 6-7 years ago. It still has good range for a BB3, and the 16's pack a punch too. IJN PBB is really nothing to write home without BB4+ crew. Fuso/Ise can be fun to play and hit hard with 12 barrels of 14L or 16D goodness. The range is short though and you will have to be sneaky and pick distracted targets.

For me 10 days(or more) would be enough, but it all depends on you. As for me, (I'm a bit impatient so)I jumped into Hyuga. Some say shes a good EBB and I think she performs quiet well. And with all those 16"L guns, she can deliver hand gloved satan to your foes doorstep and knock them off seven ways to sunday.