Every vet tells me something different... I want to know what is an absolute "must" for worms. Is it just one type or three different things..so on?
I have Ivermectin for heart-worms but that is the only thing I am clear on. Once a month heart-worm meds...but what else? If anyone can give me some idea of what worms meds they use on a regular basis and for what that would be great.

I personally don't use anything but HW protection, which also protects against round worms and hook worms.

I have never had a worm problem with my dogs.

Same here. (I have adult dogs.) I do drop off a fecal every now and then (or of course if I saw evidence or suspected a problem).

Then I would treat for whatever was there.

A puppy needs to be dewormed with something other than ivermectin 2x 10-14 days apart. I prefer Strongid myself. Ivermectin does a poor job on roundworms and hookworms,knocks them down, often not out.
Most veterinarians will dispense dewormer for oral use. Most breeders deworm, I bet your pup has already been dewormed.
Worms are encysted in muscle tissue in 90%--maybe100% of dogs. When the bitch begins to develop her mammary gland, larvae migrate to the teat. Puppies get worm larvae with the first suckle.
Tapeworms are carried by fleas and small rodents. You diagnose tapes by seeing rice-like grains around the anus. Few puppies have tapes.
Do not fear modern deworming agents, they are safe and effective, and eliminated with the feces, they have no lingering effect, and most are not even absorbed from the GI tract into the dog's body. Deworming with things like garlic
is just kinda dumb IMO when great tasting effective products are available and cheap.
I do not deworm adult dogs in the absence of clinical evidence - adults usually develop resistance to worms, and clinical disease from worms is usually only a problem in pups(or shelter dogs,rescues,mature dogs from poor environments) In a kennel situation, worms can become a problem in adults, hookworm larvae can migrate up thru the foot pads - actually,hook worms can enter human feet thru skin too, the condition is called "larval migrans"and can make itchy sores on the lower leg.
If a client really can't afford fecal+2 doses dewormer, I'd just deworm and hope for the best!

I did think that Ivermectin was for the heart worms..not for anything else. Yes the puppy did come wormed but he told me that at a latter date I had to give him three different wormers to cover all the worms. That sounded like a lot to me. I have only done Ivermectin with Zuki and one other but I don't remember what it is called and I only did it once. Is Ivermectin not for heart worms?

RIght, the ivermectin is for heartworms, the dose for heartworms is intended to kill infant worms delivered by mosquitos and prevent them from developing into adults in the dogs heart. Some heartworm medications also contain a dose of pyrantel pamonate which is adequate to kill hooks and roundworms, pyrantel is a great drug. I give my dog Heartguard Plus=ivermectin+pyrantel monthly.
I would not give a puppy special medications for Tapes or Whips (praziquantel or
a course of Panacur=fenbendazole) without fecal evidence these parasites existed.JMO.