You are going to need some specific tools for training. Use the minimum tools to get the response you need. In a perfect world no collars, leads, or other aids would be required and our dogs would know what we mean and say from the moment they’re born.
You will need a lead. The standard 1 inch wide and 6 feet long strap lead is best. Thinner leads of ½ to 5/8 inch can be used on smaller dogs. A shorter 3 ft lead can be used in certain circumstances such as heeling exercises. If you are going to be a dog owner you likely should buy 3 standard 6 foot leads at least. Hang one by each door in your 
house and keep one handy somewhere else. You can use multiple leads clipped together to extend your distances away from the dog in training “stay” and “come”. More on these in the specific training section.
A training collar is a must. This collar will only be used when training or working your dog. Yes going for a walk is training. Any time your dog is on lead you are in training and most times when they aren’t. Training collars, even if it is a standard buckle collar exactly like the one she wears everyday, should only be used during training and taken off as soon as training is over.
Part of the idea here is that the dog will KNOW when you put the training collar on that it’s business time and play time is over. When you reach for the training collar and your dog goes ballistic in happy anticipation bouncing all over and can’t wait to get the collar on, then you know you’ve reached your 
dog completely. Training is JOY to the dog and it will show. Your dog is working to please you and happy doing so.
For decades the standard training collar has been the misnamed choke chain. It is not intended to choke at all, if your dog is choking or being choked with this collar, and not responding to corrections, switch immediately to something else. The idea behind the slip/choke collar is that it will put pressure on the nerve in the back of the neck. Much like thumb pressure against the funny bone. Variations of this are the safety slip in either chain or fabric.
Up front I will tell you I am not a fan of standard slip chains/collars, this applies even more to their use on large, strong, energetic, or stubborn dogs. I use them, will continue to do so, but for the vast majority of owners they are not a preferred training collar. Much preferred is the safety type of slip/choke chain which limits the ability to choke. Never use a slip chain collar on a puppy.
Flat choke collars are available as well, either standard or safety models. The safety models are better in that they are designed to limit the amount of choking that can happen. These are chokers and do squeeze the neck, boarder is better in that force is distributed over a wider area. While not highly prevalent yet these are gaining in use on the slip chain. They are easier for the novice to use and less likely to cause throat damage. However they are not highly effective on very large, strong, or intractable dogs.
The Prong/Pinch collar has to be the collar of choice for large, strong, or intractable dogs. While the prong collar may look intimidating it may be the most humane of all collars. It works in that as it is tightened the prongs pinch the skin. The large centre ring does not allow over pinching or choking of the animal. Honestly I have yet to run into the dog that can’t be trained with a prong collar. From Chihuahua to German Shepard I’ve used the prong collar or seen it used with success and it has never failed. That is a 100% success rate. As one lady said “It’s like powering steering for the dog.” 
There is a special section on training with the prong collar. It does require a bit of learning to use effectively. Variations without the prongs are also available but you will have to look long and hard to find one of the “clamp” collars.
The Hilti Halter and Gentle Leader type halters seem to be the flavour of the month, with a lot of trainers swooning over them and these are getting a lot of press. It can an effective tool but it is not, as many would have you believe. the only collar you should consider or use under any circumstances. These both work in that corrections are applied to the snout and jaw, breathing is never constricted. A pull by the handler, or by the dog getting off line, will turn the animal back towards the handler. I’ve had best 
successes with these on small to medium energetic dogs. Some animals do not react well to the halters. Huskies and Labradors are two that I have yet to see any success in using these. I’m not saying they can’t be used on these animals, I’ve used them and they haven’t worked for me. You may have better luck.
There are so many collars and harnesses available! How are you to know what to use? Use what works for you. I strongly recommend that you have 3 training collars on hand when you start formal obedience training. A safety strap choke, a safety slip chain, and a prong collar. If I had to have only one training collar I’d take the prong collar in a heart beat.
Training collars are a tool. Use the minimum tool to get the response that you need. A 80 pound dog on a slip chain walking on it’s hind legs choking itself for a block is a sight to 
behold and indicates you have to use a different tool. Yes the dogs throat was damaged. The owner resisted changing to a different tool.
The owner was me.
Live and learn.