Framework recommendation: Writing browser based online app

I am looking for a good javascript framework to build a web app on.

In this app the user should be able to build his own level from a series of preselected obstacles.

The app should be able to:

• move and rotate objects on a really small grid.

• Draw lines between the obstacles by having the user click on points inbetween them.(drawing a smooth line from these points and allowing the user to move the points to later adjust the path)

• calculate the length of those lines The size of the level should be an option the user can choose. (no fixed aspect ratio)

• a plain, easy to use interface

• Render an image of the entire user generated level. (if not possible I will need to find a server-sided solution)

• The objects need to able to be scaled (sprite size increased or decreased)

• doesn't need to rely on the server for logic too much.

• Needs to be able to use HTTPS to keep things secure

• run on android and ios too.... I believe this means WebGL won't suffice.

Users need to be able to register an acount so there data can be securely saved in a database. (require a password to acces user resources)

it does NOT need sound

The app will be in touch with the backend for storage of the users data. The backend will probably be a REST-like architexture with authentication.

With this in mind, what would be a good client framework in which I can program these things without having to write huge handelers myself?

And if you make a sugestion: What backend works best with the framework you suggested?