Tokyo Subways busy around 17:00-20:00?

I'm coming on April 8th a Sunday to Nartia around 4:30 i'm going to take the Narita express to the Tokyo subway station.
Is it usually busy around this time? (Tokyo Subway Station)

I'm bring only one luggage, i'm not sure if I should send it through Takuhaibin or am I fine?
I don't want to take up a lot of space on the subway with my luggage.

In the subway stations are there escalators? or only stairs?

Tokyo Station tends to be busy almost all the time, but you arrive on a Sunday, so the usual worker bees wouldn't be around to use it. Most, if not all, tracks have escalators. I Haven't used all tracks, so I can't be certain. There are even elevators. This is the map to Tokyo Station. http://www.jreast.co.jp/e/stations/e1039.html

You should be fine with your luggage. You're not the only who will have used that station!