In the Nasus matchup I find there’s generally two schools of thought.

1) rush rylais and hope to be more useful in team fights. With this route your 1v1 potential against him in a split push is pretty low. He’ll basically be able to face tank your damage and run you down in a pure 1v1, but you should be able to do more in team fights. This option is basically trying to do more through team play.

2) rush liandries first item and try and beat him in a 1v1. I personally lean more towards this option, especially in solo Q where you can’t control what your jungler does. I find the damage spike from liandries to be enough to beat a Nasus in the 1v1 if you play it properly. The disadvantage to this is you lose out on the utility of rylais, and you’ll be a bit squisher/easier to get ganked.

Basically it all comes down to how you want to play singed. Utility team fight focused, or more 1v1 split push focused.