Fitting a western saddle to a thoroughbred

I have a thoroughbred and I am looking for a western saddle that will fit her properly. I previously rode English, so I am unfamiliar with the parts of a western saddle. Could someone explain the following to me?
Rigging: what is this, and why does it matter.
Gullet: We have these on English saddles, but they only come in small, medium, and wide. On western saddles it seems as though they actually have measurements. I think I will need a 6 inch gullet for a high withered thoroughbred. Is that correct?
Bars: Ok someone told me these are what actually rests on the horse's back, and can be quarter, semi, or full. Again, dealing with a relatively narrow backed thoroughbred, do I need quarter bars?
Thanks!
PS: If anyone knows of a good saddle brand that can accommodate a thoroughbred, please let me know. I don't have a fortune to spend, and I like synthetic saddles because they are lightweight.

I suggest reading here:

Complete guide to the american western saddle

And here:

Saddle Fitting: Free and easy saddle fit help from the experts

Okay, the gullet measurement measures the space between the pommel, where the horn sits. When fitting TB's, you also have to consider how high the pommel itself is. A good place to start is with a 6.5" wide gullet. Or, take your current English saddle and measure from d-ring to d-ring (or if your saddle doesn't have d-rings, from pommel nail to pommel nail). Bars are what actually sit on the horses back, so what size bars you need generally are dictated by how pitch-y your horses back is (do you have more of a WB/QH thoroughbred with a broad back, or a shark fin TB) since you say he's relatively narrow, you probably need semi-quarter bars.

I don't know about specific brand, but in general barrel saddles fit TB's better than any other. Of course, if you can find any western saddle with the above specifications, its more than likely going to fit pretty well.

As a TB owner, I share your pain! Even moreso because I like leather saddles, but I don't want them to weigh a ton....my search is ongoing.

On the flip side, you can take a tracing or a mold of your TB's withers and about midway down his back (where the middle of the saddle would sit) and take it to your tack shop to hold up against the saddles there.