As i’m only 14 and already have a dog and a lot of fish. My parents don’t like the thought of getting another pet. Although I would pay for EVERYTHING and they wouldn’t have to lift a finger or pay a penny. I just don’t know how to convince them

Any ideas?
I have 2 budgies, they can live for quite a long time so what are your plans when you move out or go to college? How much do you know so far about birds (diet, lifespan, cage size, perches etc.)
I suggest you go over to Avian Avenue (a forum about birds) and have a look they will help you. They are a very expensive pet and need a large flight cage, expensive (but necessary) vet bills, variety of food (only seeds is absolutely NOT viable), range of foraging toys, natural perches.
You also need the time to tame them and spend time with them, budgies are either very affectionate or not that affectionate at all. Either way you have to accept it so keep that in mind. It takes a lot of time to tame them and their bond with you can easily be broken.
One of my budgies started acting sick, I had to take her to an avian vet and now I have to medicate her twice daily. This has been incredibly expensive but this is what you sign up for if you choose to get a bird of any kind.
How do you plan to give your budgie out of cage time, it needs to be supervised?
If you have a dog, don't assume they will get along
Don't get me wrong, they are small and are an amazing pet however, if you want to care for them properly it takes a whole lot of effort.
If this is your first look into the world of birds maybe try volunteering at a bird rescue or something to see if they really are for you. I've had four budgies so far (two have passed away), only one was as affectionate and people obsessed as I thought they would be.
Budgies (in my experience) are quite independent birds compared to a cockatiel or a GCC for example.
Lets say, you bought two budgies and one passes away. What do you do with the other one? This is a hard cycle to get out of. They are flock birds so really do need a companion anyway.
Hope this helps!