How do I select and move an object in GIMP?

In the tool box is a tool called "Move Tool".

Click this tool, then drag-and-drop the object you want to move. This assumes you still have layers (and the object you wish to move is a defined layer), and have not flattened the image. It can be tricky trying to select the object to move, but it can be done.

GIMP is for raster graphics. It means it doesn't know if it's a rectangle, circle, line or Mona Lisa that you're drawing - it treats everything as a bunch of pixels. Think of your image as of a painting: once you paint something on that rectangle, it's covered with a paint of different color. If you want to enlarge it, you have to grab a brush and do it manually. If you want to move it, you have to paint it in that place and paint something else over the first one to cover it.

If you want to have an object that you can move around later in GIMP, draw it on a separate layer. You can also use vector graphics program like Inkscape for that - vector objects can be moved around in that manner, but editing such images has totally different feel that with rosters.