Nice looking dog!
Ahhh, kids & stickers, surprised they didn't decorate their new buddy!
Good on you for the snip & chip, both of my guys had that done at 5 months.
You will find a lifetime of info if you Google NILIF, or Nothing In Life Is Free. The idea behind this is that everything is earned. Pack leaders control resources, this is why you will many times see the smaller dog in a group being the top dog, it isn't about size or strength. It is also the key to a comparatively small person having no problem handling a very large dog.
Clicker training is another excellent training tool, taken from dolphin training. The click from a clicker is consistent from person to person, and signifies that a treat has been earned. Get used to having a clicker in your pocket, I keep a length of cord on mine to keep it handy on my wrist. These are cheap little gadgets available at most any pet supply outlet, I have many kicking around the house. Start with a handful of kibble, click & feed one, click & feed one. They associate the click with a treat real quick, feed an entire meal this way if you like.
You have a good start with one of the most important things; sit. This is the basic start for earning anything; food, toys, access to areas, anything & everything. From the beginning explain to everyone involved with the dog the exact meaning of commands, down is very often misunderstood. With my guys down means lie down, off means 4 on the floor, no matter where you might be. Consistency is key, if the smallest kid with a goodie has the dog sit before offering the treat that little kid is controlling resources.
Food is a major resource for most dogs, sounds like yours is no different. Once you have the sit for a treat, you can teach leave it. You put the treat on the floor at a slight distance, if the dog goes for it pick it up, start with sit again. Leave it will soon translate to cats, rabbits, or anything else you don't want them to mess with.
With walking, I always start with if they pull I stop. I'll stand there until they stop pulling and take a step, if there is no pull I'll continue. If they pull I stop. They catch on soon that pulling gets you nowhere, and they focus on you, waiting for that step. Always start consistently with the same foot, which is usually the left foot since a heel position is on the left.
For a real serious puller, or smaller breeds where there is a risk of trachea damage from pulling hard on a collar I use a harness. For hard headed cases (some terriers!) I use a short leash with a harness, a longer one with a pinch collar. The pinch collar is for corrections, when they pull on the harness. Don't be put off by the looks of a pinch collar, put one on your arm in a shop, give it a snap. It is an attention getter more than anything, nothing painful. It's safer than a choke collar, which few people ever use correctly.
With all of these things use a click & treat for a job well done. Also, get the younger kids to understand that the clicker is a tool, not a toy.
If he has lab in him he should be pretty easily trained, I've had terriers for many years, independent thinkers. Sometimes you have to make them think that it is their idea, not yours to do what you want. All dogs go through what can be best described as the terrible twos, just like kids. In these cases, it's a longer leash, you are attached to my belt, and you get constant supervision & training. This often makes tasks take a bit longer, but it is worth the end result. It makes every instance available a training situation.
I am also a huge advocate of crate training. This is the dog's safe place, his den, and works off of the den instinct. There will be times when you won't be home, especially when the dog is younger, where you don't want to risk him getting into things. There will be times when you are home, when activities dictate for the safety of your dog, he needs to be in a safe place. Around here it's usually home improvements, or my son loading more furniture into my house for his anticipated home purchase. Being accustomed to a crate also helps the dog if he ever needs to spend some time at the vet, accidents happen. Crate training is a huge housebreaking asset, taking advantage of a dogs natural aversion to soiling their sleeping place.
I start with a crate just big enough for the dog to stretch out & lie down, being able to turn around. A soft bed, scrap of rug, anything you have or can get to make him comfortable rounds it out. Toss in a treat, let the dog see it get tossed in. He may hesitate at first, this usually doesn't last long. Next, out of eyesight of the dog, toss in a treat. He'll find it, and get used to checking regularly. Don't be surprised if he gets tired of waiting and lies down on his own. Calmly swing the door shut, this generally doesn't make them nervous, as they are in there on their own already. Treat, as long as the dog is calm, and swing the door open. If the dog comes out, toss in a treat close the door, & repeat. They soon associate the crate with a nice place to sleep, goodies appear, and it is, like a kid, their room.
While I would like to second that pic for POTM, taking another look it isn't the pet! I would like to nominate the picture above it, I don't know which I like better, the eyes or the ears!