When do I get the first companion

You can make the decision when you leave the starting planet. You also need to be at level 10, you may not be level 10 at when you reach this point so you'll need to go back if you leave that area.

To leave the starting planet/area you need to complete all the story quests.

This is an old question but the current answer is now out of date.

As of Patch 1.2 the game supports the ability to move around most or possibly all of the ui elements that appear on screen and in general has a lot more customisation options than at launch.

http://www.swtor.com/info/media/trailers/quick-look-ui-customization is an official video demonstrating this.

You can access this through a small button just above the lock toolbars button on your toolbar or through the main options menu (ie where you'd go to select change preferences).

It includes three different defaults that you can use either as is or as a starting point ofr your own customisations.

The three options are a simple form with one action bar, the extended quickbars which gives you all the quickbars active and one that seems very similar to the standard WoW layout that I think is called "Classic" or something similar.