What size saw blade should I look into for cutting letters out of a 1/32" sheet of metal (I think steel) with a saw
If I understand what you are attempting to accomplish, this is exactly the right type of project for a jeweler's saw.  You use a technique called piercing to cut out those type of interior shapes.

I found what looks like a pretty good tutorial here, but the basics are:


Using a very fine drill bit, create a pilot hole somewhere inside of the shape that you want to cut out.  Make sure that the pilot hole is large enough that your saw blade will be able to fit through the hole.
Attach your saw blade to the handle at the bottom, but leave it unattached at the top.
Feed your saw blade through the hole in your piece of metal, and then attach it to the upper part of the saw handle.  
Begin sawing towards the outer edge of the shape (in this case a letter), and once you have reached the edge, saw around the outline until you have removed all of the interior material.  In this picture, you can see her pilot hole, the straight cut to the outline of her shape, and her continued cut line around the perimeter of her shape.




One big challenge with your particular project however--jeweler's saw blades are extremely thin and easily broken. You need to be very careful not to bend them at all, but instead always keep your saw frame in basically the same orientation to your body--i.e., the blade is always facing in the same direction, and you are always sawing away from your body.  This means that you need to move the piece of metal around as you cut out a shape.  This gif illustrates how to move the metal. 

It looks like the piece you want to cut may be too large to move it in this way. You might be able to follow this exact process using a really deep fret saw frame instead of a jeweler's saw frame. I have never used one, so I don't know if they can handle blades as fine as a jeweler's saw blade, but they have a much deeper frame, which might work better for a larger piece of metal like the one you show here.  

Fretsaw:
 

Don't know what all of these saws are, but the two saws at the lower right are both jewelers saws, so you can compare the frame depth with the fret saw shown directly to the left.


EDITED TO ADD:  I completely forgot to answer the actual question about the size of the saw blade. The size of the saw blade is dependent on the narrowest area that you want to cut out.  Since none of the areas in your image are particularly fine (compared to the width of the saw blades), I would use the thickest jeweler's sawblade that you can use, to limit breakage.