Yes, you'll be free to move but must return to within 10 feet of where you entered
From the description of the Ready action in the PHB or the Basic Rules:
First, you decide what perceivable circumstance
will trigger your reaction. Then, you choose the action
you will take in response to that trigger, or you choose
to move up to your speed in response to it.
Moving to the Ethereal Plane is certainly perceivable, so it works as a trigger. As per this QA, there is nothing about being in the ethereal plane that prevents you from taking a reaction.
As for limitations on movement, the DMG has this to offer on the Ethereal Plane:
A traveler on the Ethereal Plane is invisible and
utterly silent to someone on the overlapped plane, and
solid objects on the overlapped plane don't hamper
the movement of a creature in the Border Ethereal.
The exceptions are certain magical effects (including
anything made of magical force) and living beings. This
makes the Ethereal Plane ideal for reconnaissance,
spying on opponents, and moving around without being
detected. The Ethereal Plane also disobeys the laws
of gravity; a creature there can move up and down as
easily as walking.
So you can move up to your speed, you can move through any solid objects, and you can even fly, but you can't move through other creatures (or force effects). Unfortunately, Blink stipulates:
At the start of you next turn, and when the spell ends if you are on the Ethereal Plane, you return to an unoccupied space of your choice that you can see within 10 feet of the space you vanished from.
So you can spy through walls with Blink, but you can't travel with it.
It depends on how you travel to the Ethereal Plane.
Nothing about the Ethereal Plane's description indicates that objects are forced to leave, but how you get there matters.
As I see it, two categories of planar travel are relevant to answer your question.
Permanent travel
This includes Portals, spells like Plane Shift, and traits like a Phase Spider's Ethereal Jaunt.
In all these cases, magic brings you to the Ethereal Plane and then no longer affects you.
Someone with Detect Magic in the Ethereal Plane cannot sense any ongoing magic on you related to the planar travel, because there is none.
In these cases, you and anything you place in the Ethereal Plane are there permanently and can't leave unless another magical effect lets you.
Temporary Travel
This includes spells such as Blink and Etherealness.
In these cases, magic brings you to the Ethereal Plane, and keeps you there for a duration.
Someone with Detect Magic in the Ethereal Plane can sense the ongoing magic that keeps you in the plane.
When the magic ends, you and everything you brought with you return to whatever plane you were in before entering the Ethereal Plane.
In particular, both Blink and Etherealness have a range of self. The objects you carry are not the target of the spell, they just travel with you because you are carrying them. Both these spells cannot target independent objects, so if you are no longer carrying an object then it is no longer affected by these spells and it will return to whatever plane it was in before entering the Ethereal Plane.
Best Answer
RAW does not specify, RAI clearly yes
The spell only says that you are transported to the Ethereal Plane. Taken strictly and literally, it would mean that you leave all your stuff, including clothes, behind on the plane you start from.
This kind of behaviour would be highly unusual from a D&D 5e spell. You are not expected to account for these things. Spells that transport you are understood to also affect the gear on your person. Some impose limitations, but usually about items that you would not be able to hold.
Also, this concept of "ownership" is absent from the mechanics. You are either holding an item or not. This is in line with the practically expected behaviour of "take even what is bolted down" characterising most adventurers, especially in dungeons.