Good luck with the new pup!!!! He does look like a terrier and a lot of terriers are very intelligent. Some of my best trick dogs were terriers. I have always wanted a therapy dog and I always end up with a trick dog instead. LOL. It is okay though, I love to teach my dogs how to do things.
Does he know sit? Lay down (down command). Off command (not to jump on people). A lot of people use down for both, I use down for lay down and off for not jumping on people so they are different. Also, teach him a come type command but most trainers recommend you use a word like "touch" or "recall" I personally hate recall because I am not going out on the street and yelling "Recall" to my dog. LOL. I will tell them to "touch" with 2 fingers pointed straight down at my side and my dog needs to come up to me (taller dogs need to touch your finger tips) and I get down on the ground and grab their collar slowly and give them a treat. This is an important command because if he runs off he will know to come back and you will grab his collar. Then praise praise and praise him for coming back, never yell at him for running out the door in the first place. Give him a treat even if it means going inside to get one and just keep telling him what a good boy he is. If you reward the dog for coming back you will get a lot farther than if you punish them because they ran out the door or whatever they did to get loose. I usually just yell the word "treat" and mine come running back inside the house. LOL
I also teach mine not to cross the door thresh hold without permission. A good skill to teach a dog. My new rescue got out 3 times the first week, but we have a gate on our porch so he couldn't go far (although given a chance she would fit through the gate) and so I worked with her and now she knows not to run out the door. I just say "inside" and they all know to stay in the house. It just take time though. I don't know what his behaviors are like or what you need to work on, but those are some ideas.
I highly recommend a training class either with a personal trainer or going to a class at Petsmart. A trained dog will make your life so much better. I am able to do basics with my dogs and teach tricks only because I have taken so many different dogs to training classes that I have a pretty good idea how to teach the basics. I have never not had a dog in my life, usually 2 of them (having 4 right now is crazy, but fun).
Good luck and I really hope he works out for your family! I have 3 rescues at my house. Almost every dog I get is a dog that someone else wanted to get rid of. The exception to that is my Yorkie puppy (he is 2 1/2 years old) whom I got at 10 weeks old from a friend. He know over 20 tricks and is very well trained. My other 2 yorkies were rescues I took in at 9 years old (he is almost 12) and 7 years old (I have had her a month) and then we have an almost 7 year old English Setter who we got when he was 15 months old off Craigslist. He is the dog we have currently had the longest even though he not the oldest. He is also very well trained, by me of course.
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