Congrats on the new purchase.
I guess the first thing, as Katherine notes, is to accept that a Walker is a horse. As a rule treat it like any other horse. There may be a difference or two, but they are minimal.
Regarding saddles, “gaited horse saddles” are more of a marketing initiative than an operational concept. Find one that fits and you’ll do OK.
But finding one that fits will be a big problem for you with a really thin horse. And if you find one it won’t fit when the horse fills out. You might need two, three, four or more during the rehab process. Maybe the more practical (and economical) approach is to go with a bareback pad and keep the saddle work light and in the arena until the horse fills out.
As to why folks let horses get like this, the reasons are legion. Family problems, financial problems, lack of skill by the owner, lack of knowledge, a mean spririt, or a difficult equine temperment are all reasons. None are excuses.
Have you done a Henneke Scale score? If not, do one. Measure and photograph. It will make a nice “scrapbook” and keep Animal Control off your back if a nosy neighbor decides to call them because of your “starved horse.” Sadly, this sometimes happens.
Lots of ground work will be rule until the horse becomes strong enough and fit enough for work under saddle. If you don’t know how to longe, long line, etc. now’s a good time to add some new skills for you! 
One thing you may find is that the horse you have now will not be the same horse you have in six months. A starved horse without the energy to express itself may turn out to be very “expressive” when properly fed up. Indeed, one reason people sometimes “functionally abandon” horses is that they are too much for them and rather than sell them they just lose interst and “warehouse” them (poorly).
Good luck and keep a record of what you do. It will make intersting reading in the future, keep The Authorities off your back for now, and can help educate others in the the process.
G.
