Allegro 5 graphics routines take floats as parameters. In GUIs, coordinates are usually expressed as ints.

What is the better approach, in your opinion? should the widgets' coordinate properties (position, size, thickness etc) be specified as floats or ints?

Mouse coordinates in A5 are still integers, so I say go with integers. Then you don't have to waste time with a bunch of casts in hit tests. The drawing routines take floats though, so you would still have to cast/adjust those.

I think the bigger question is whether or not you want to support transformations. i.e., Should somebody be able to set up the screen to go from (0,0)-(1,1) and it still work with your GUI?

If the answer is no, then just use integers.