is a leather horse bridle the right material to be looking for?

  You're comparing apples to oranges.
 
  The complete western nylon bridle is inferior in all ways.  The bit is going to be lightweight, poorly balanced and not a good tool to use on any horse.   If you bought this set, the first thing you would do is replace the bit.  The rest is a personal bias but nylon reins are lifeless, stiff, coarse in your hand...  The leather bridle is first off draft size.  You pay a premium for O/S and draft tack.  The leather is superior in quality, double stitched, soft...  There is alot between the two but the bottom line is quality always trumps price.  I have bridles that have lasted me 25+ years.  I also have nylon and leather ones that should be in the trash.   
 
 Check out CL.  There's always good quality tack of sale on there.  Check out this site's bridles.  They have a decent selection of good working headstalls (start about page 3).  With leather there can be a huge disparity in what you're getting.  There is alot of inexpensive, inferior Pakistani/Indian leather out there.  It's stiff, brittle, over dyed and pretty easy to identify.  Look for the words harness leather or latigo leather as they normally imply US leather and  US made. 
 
  Let us know what you want and one of us probably has something in the barn that we don't use that would fit the bill.

Jade,
I use both nylon and leather tack. I have a couple different nylon headstalls that I am very happy with and plan to get more of them. I also have a leather one that I really like. I have one nylon one I don't like. I use a couple different kinds of nylon reins also. I haven't been able to find leather reins that I am happy with. I have one leather set that I just got that may be ok with a minor modification.

I personally do not like synthetic saddles.

2manyhorses makes excellent points about quality and leather. There is a lot of junk out there.

We use both around here. In some cases we have a nylon headstall with leather reins. Pretty much the nylon reins we use are barrel reins. The nylon split reins felt rough and uncomfortable. We also have some synthetic reins and a synthetic saddle that have held up very well. As 2manyhorses said about the bridle with the bit, we change the bit. Those that come with the set are cheep and really only good to decorate your wall with. My favorite sets we have are the Reinsmain headstall with matching reins. I bought two of them in different colors five years ago and they still look great. When we got them they didn't have the clips. You could take them off. Here's the headstall:&nbsphttp://www.horse.com/item/reinsman-quick-clip-browband-training-headstall/WCA03/ 

2many pretty much said it all.
I am a leather girl.  I find it easier to adjust and punch holes in and more durable.  Even my barrel reins are leather.  Nylon is good if you want color and washability.  It is a matter of preference.
 
I REFUSE to ride in a synthetic saddle.  I do not care for them at all and they are cheap for a reason.  JMHO.
 
If you can go to a tack store and look around, you will want to feel the different leathers, nylons, etc. and you will feel the difference in quality.
 
A&nbspenny saved now can lead to more spent later to replace something.

I have several nylon headstalls and don't have a problem with them. However, I always use leather reins -- just prefer the feel of leather in my hands.
 
I don't care for synthetic saddles either, although I've had a few good ones. These days I always buy used NAME BRAND leather saddles -- the quality is so much better.

Don't discount bioethane for bridles (I think I spelled it right).  VERY practical and can be washed with soap and water.
 
I second the idea that someone might have something laying around that would work for you.
 
I have a local friend who makes very affordable leather bridles.