I've done a lot of both with rescue dogs. HW is not the end of the world -- it's treatable. As "surprise" illnesses go, I prefer it over tons of other possibilities because we know the dog's chances of a complete recovery are excellent! As long as the dog is early in the disease (not caval), it is likely to recover and be just fine.
Immiticide treatment (fast kill) is the gold standard treatment. If you can afford it and the dog is strong, it's the fastest way to rid the dog of HWs. There's a good argument that you want them out as fast as possible because they are damaging the pulmonary arteries, lungs, and heart as long as they're in there.
In a young, healthy dog, the chance of complications from fast-kill with immiticide are low. It's a hard 3 months, with intense restrictions on movement (strict crate rest), but it's so hot and humid now it's not like anyone really wants to go outside anyway!
HOWEVER, I have had one foster dog die during fast-kill treatment (she threw a clot in her lungs, had multiple trips to LSU's emergency ICU clinic, got about $3000 in treatment to try to save her...and still died) -- it is not a "risk free" treatment. It would be wise to know the route to your nearest emergency clinic with an ICU (oxygen cage), just in case. It's arsenic based, and it's a tough thing for the dog to go through. Be very realistic about what it will mean: NO exercise, STRICT crate rest, leash-walk in your yard to potty, etc.
The cost of fast-kill (immicide) treatment varies immensely from clinic to clinic. I know one vet who does the series of 3 shots for $300 for a GSD-size dog. Another does it for $500. And a bunch charge $1000-1500. They all use the same dose of the same drug! No matter how much you like your vet, I'd call around to verify the price quote is reasonable, just for peace of mind.
If you consider slow kill, the ONLY way I do it is with ADVANTAGE MULTI (not Heartguard). We've seen dogs test HW neg in as few as 9 months using Doxy + Advantage Multi. (The longest I've seen it take is 18 months --12 months is probably average in our experience.) The two dogs that I personally know who tested HW-Neg in 9 months with no treatment except Doxy + Advantage Multi were older dogs--huge surprise as they had likely been HW+ a long time. I know LOTS of dogs who tested negative in 12 months. That's less than the HW life cycle so it's almost certain that the Advantage Multi is shortening the lives of the adult HWs--despite what the old research about using ivermectin says.
Advantage Multi works differently in the body than ivermectin because it builds up a steady-state in the blood after 4 months. That means the worms are constantly bombarded by it. That's the best theory any of my local vets have as to why it's killing adult HWs when the other HW preventative products are not. It's not used this way most places -- it's something I know of vets using regularly in South Louisiana (but not New Orleans).
Finally, there's some good, recent research demonstrating Advantage Multi does have some effectiveness against (young) adult HWs--a vet journal article came out in 2014 that you should discuss with your vet (one of the co-authors is Dr. McCall, a well-known HW researcher and former member of the HW Society's board):
Chandrashekar et al., Experimental Dirofilaria immitis infection in dogs: Effects of
doxycycline and Advantage Multi® administration on immature adult parasites,
Veterinary Parasitology 206 (2014) 93–98
I think the decision should be made with your vet based on your finances, the overall age and health of the dog, and severity of infection (e.g., are there clinical signs of HW disease yet)? There are times when we HAVE to do slow-kill with Advantage Multi because the dog is too weak to go through immiticide treatment (esp. with seniors). There are times when we HAVE to do fast-kill with immiticide because the disease is advancing and the dog doesn't have much time unless the worms are killed quickly. Then there are times it's a cost-benefit analysis and either decision is defensible. You've got to talk this through with your vet, since your vet is the one looking at the x-rays of the chest, listening to the heart and lungs, and looking at your dog's bloodwork.
Either way, you can save some money by asking your vet to order Doxycycline compounded for you -- Wedgewood pharmacy out of NJ sells it in 400mg chicken-flavored tablets that end up being A LOT cheaper than a large supply of the 100 mg generic capsules. Roadrunner pharmacy out of Arizona also sometimes has good pricing. Your vet will have to check the pricing for you -- they won't talk to you directly. Here's a link:
Veterinary Pharmacy, Wedgewood Pet RX