I feel your pain, having had a dog with a torn CL. I also literally feel the dog's pain, having a torn ACL myself. First, x ray won't show the tendons or ligaments, the torn ligament is diagnosed through a specific motion test called "drawer" motion as well as clinical signs. MRI can diagnose too. The "Drawer" test is often not conclusive until the dog is under anesthesia as the tense muscles inhibit the forward motion of the leg that comes from the torn ligament no longer supporting the patella. If they are basing the diagnosis off an x ray, I would be a little leery. Soft tissue doesn't radiograph well. Are you certain it isn't a patella luxation? That would be seen on x ray, torn CL would not be.
Here's what to expect. The surgery is expensive, as you know. Best case is to be referred to an orthopedist, don't let someone without a LOT of experience muck around in a joint. Too much risk. Expect to go home with a painful dog, expect extensive rehab in order to have a successful outcome. Swimming is ideal once stitches or staples are out. Recovery is harder if the animal is overweight. Depending on personality, it can be hard to keep the dog quiet as much as will be necessary, so be prepared with plenty of things to chew, etc to keep her occupied.
Understand the risks....most importantly is that in roughly 65% of cases (and that's a low estimate, honestly) the other leg will also blow its ligament within the next few years. So you may be doing this all over again in 6 months, or 3 years, but chances are good you will be doing it again.
I'm not trying to discourage you, just want to make sure you are as educated as possible. She will most likely always be painful on that leg, the arthritis will eventually form particularly if the surgeon is not painstaking in his/her efforts to cut away ALL of the torn ligament, any small piece left behind will irritate the joint capsule.
FYI I'm a vet tech, I've worked for a vet who did CCL surgeries (because in dogs its often the cranial ligament, not the anterior as in people) almost daily with great success. I'm not a vet, I'm not an expert, but I wouldn't butt in if I didn't feel like I could offer something useful to the conversation.
Good luck. Its not an easy call. Don't rush into anything.