When I bought the starter kit for my son for Christmas, I really didn't look at what is all in it. I know has anyone played the campaigns? Is it important to use the premade characters? Really I'm just really worried that we will burn though these and feel abit unfulfilled. Anyone used the starter kit, and have some advice on the storyline?

I have not played the campaign but I have read through it, and I can tell you that it is certainly not important to use the premade characters. They're just there to use as reference, and in case you don't have time to make a character and need one quickly.

The Starter Set is an extremely good entry point, and has everything needed for at least I'd say 6+ sessions of game with the included adventure, which also introduced the game in an easily digestible way, both for new players and masters alike. You also get a set of dice, which is always nice (and one can never have enough of those :p).

The premade characters, while well designed (but not really optimized in terms of numbers [not that it matters enormously for newcomers to the hobby]) are not at all necessary, and the few bits of story that might be useful to have one or more playing characters to have weaved into their background are presented at the beginning of the adventure, so that they can be included easily even with newly created characters.

Other than that, it's all just fun, and when you are done with Lost Mines of Phandelver you should already have at least a few leads the party might want to pursue, therefore opening up to home made adventures (for which you already have a good amount of reference and materials in the set itself) or other published adventures (Storm King Thunder seems like a very good an natural continuation from Lost Mines I've heard).

Keep us updated on how your son likes the game, and if you need any more advice or help, the community is here for everyone :)

I've DM'd most of the Starter Set for a family game; we aren't quite through due to the challenges of finding times we are all available.  Using the pregens is not required, although I do think it's a wise idea for a lot of beginners.  The backgrounds tie them in nicely to the story.  If you are DM, you need to read through their backgrounds.  Character creation can be pretty daunting for new players; just grabbing a pregen and using when first learning simplifies the process.  That said, some new players may want to create their own characters.  My son did.  (The Starter Set was his Christmas present 2 years ago.)  My husband and daughter used pregens.  (They both played two characters to help with party balance.  It worked for them, but it's not something I would recommend for new players generally).  D&D Beyond does make character creation a lot easier, and if you stick to the clasees, races, etc. from the Basic rules (used by the Starter set), you don't have to spend any money to do so.