You have to work with your mom and her fear. Of those breeds you mentioned, I would highly suggest the lab. Big hounds have that deep, resounding OOW! And they and beagles, no matter how well trained can be very distracted by smells. I have a soft spot for labs. My baby I adopted when he was six months old. Now he is eight. He is my best baby in the world.
With your mon's fear, pugs are the way to go. They aren't the best running partners with their short legs, but are VERY active dogs, and need to be high activity to keep from getting horribly fat. Look up and like "Steve the Pug" on Facebook and you will see a very active healthy winning pug. He "runs" a lesson program in ohio. Being a barn manager is hard work on a pug but somepuggy has to do it. They are kind, loving, as active as you want to be, not as stubborn as people think if you take the time to train them, and they are so darn cute. They are far from intimidating.
Something you must do is enroll in obedience classes, preferably with a local person, not Petsmart. Whether or not you can train your dog yourself, this might help gain some faith in your mother that you are definitely working on getting him an education. She might not see you doing it in your backyard, but she will notice when you put him in the car and drive to his class. Assure your mom that these classes will make him perfect. Talk up your instructor. For example, mine was number two in the country for some time with Great Pyrenees. She also had many awards for obedience and shows from across the country. Neat woman! Plus, classes are a blast.
Do not under any circumstances get one without your moms blessing. Nothing is worse than a surprise puppy. Write up a plan. Write up your promises(and KEEP them). Write up the benefits. For example, if you are running down the street, you are less likely to be grabbed by some psycho off the street because people fear dogs. He will be a big physical deterrent to attackers even if be is the sweetest dog.
Include your mom in everything. Shopping for supplies. Even see if she would come to the shelter with you(Stress that you will be SAVING a life). Most places have rooms where you can meet the dogs individually so she wouldn't have to walk through the kennels. Plus they are all secure in their enclosures and can't get out.
And go SLOW! Plan to get your dog... Three months from now. Set your goal far away and work slowly on carefully removing this barrier. Busting through will cause a mess. You want to do this calmly, and carefully, and neatly.
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