Hey I don't comment much here anymore, but since moving back to NM I try to respond to anything in the area if I can help. Fires or not fishing is tough in the Gila. If backpacking is your main focus, you are going to the right place. Its one of the most amazing places to visit. The isolation and remoteness means very few backcountry visitors compared to most other backpacking spots in the lower 48. Snow lake is stocked, and the adjacent streams (Gilita creek, etc.) have fish, including the Gila trout. You must have the free Gila trout permit along with your license to fish certain streams where there might be Gila trout. The particulars are listed at NMDG&F.
Your line weight isn't as critical as rod length. I fish many very small streams here in NM. A 7'-6" 3wt. is too much for a fish that can fit on one hand, but what makes it difficult is fishing a stream that isn't as wide as my rod is long. Special casts are required. Sometimes no casts are even possible. Still fun though. The Gila river itself is wider and provides more casting ease, but could be fairly stained right now.
Flows are increasing now so when you go will be important especially if you plan on crossing streams to get into the back country, which is basically how you do it in the Gila.
Sit in a hot spring if you can. Turkey creek hot spring is truly amazing.
Good luck.
BH.