Collar or harness for a 3-month-old puppy?

And stick to a fixed lead under 6ft (2m) long to start with. Depending on the dog's size and strength, go for either nylon or leather.

It's all in the title - collar

Yes, I agree—a collar is definitely better than a harness, and retractable leads are a big no-no. When you recall her while she's pulling, give her some praise, but don't go overboard or she’ll get too over-excited. Most importantly, make sure to praise her before asking for a "sit" or a "down". If you only reward her after she's sat, you’re rewarding the sit, not the fact that she’s come back to you and stopped pulling.

It’s quicker for some dogs than others, but patience always pays off in the end. It took me nearly a year to get mine walking calmly at my pace, and even now she still forgets herself occasionally. But these days, as soon as the lead goes taut, she springs right back to heel without me having to say a word.

It’s also a good idea to always keep her on, and have her return to, the same side.

Harnesses are best avoided, particularly for puppies, because if they are poorly fitted, they can cause elbow deformities (elbows 'bowing out' from the body, which changes their gait). Besides, as @Docline pointed out, harnesses are designed for working or sporting dogs; unless a dog has a sensitive trachea (as is the case with Sirius), they aren't really necessary.

Learning to walk on a lead takes patience and consistency. If the puppy refuses to move, you can crouch down facing them with the lead slightly slack and enthusiastically encourage them to follow you. Puppies are generally very responsive to this technique. Clapping your hands and making excited noises (even if you look a bit daft to passers-by, lol) quickly gets them to follow their owners.

For a puppy that pulls, @Docline’s method might be a bit of a long road, but it’s very effective. It’s a gentle, force-free approach that teaches the puppy to focus on their owner.

Lead training just requires a simple collar and a standard lead (definitely no retractable ones).

It’s a bit of training that takes some time. Docline has already covered the basics.

Harnesses are designed FOR pulling.

What every dog needs to grasp as soon as possible is the difference between two types of walking:

Free-walking (or on a long line) where they can sniff whatever they like / walking to heel where they must match the owner's pace and can't keep their nose to the ground.

The best connection between dog and owner is achieved with a standard lead, or a slip lead if you know how to handle one correctly.

The lead should be held vertically, kept slack, and short.

At the beginning, reward every correct position.

Don't move any more than a statue would if the heel position isn't right.

Learning to walk to heel on a lead should be done in short, frequent sessions.

But before that, your dog needs to have already learnt to always follow your legs through the right kind of play.