How to introduce a cockatiel to 2 budgies

Hi, so, I’m looking into getting a cockatiel and am currently in the gathering information phase. I’m thinking of getting a female cockatiel to go along with my currently I have a female and a male budgie and the cockatiel will have its own cage. I heard you need to keep a new bird apart from your current birds before the introduction and am planning to keep her in the bedroom for 2 weeks before moving her to the living room. Would I have to keep her in her cage for at least another month before I try to get her out while the other budgies are In their cage (closed cage)? The cockatiel in question would most likely not be hand tame.

I appreciate any tips

Two weeks apart is not long enough it really should be at least 30 days. Budgies can be very nasty birds with other species. I have seen Cockatiels that are missing toes due to being housed with Budgies. I have also seen those that get along fine. It's a gamble when bringing in any new bird. I know first hand as pretty much none of my birds get along.

As you have a pair of budgies I wouldn't bring in a third bird. Your budgies may not take kindly to a third wheel. There is a good chance that they won't get along and will have to be kept separate all the time. Do you have the time available if you have to keep them separate all the time? Will you have the time to have the budgies out and then to have the Cockatiel out if they can't be out together?

As for taking the bird out of the cage it's not a consideration of time but of trust. You have to build a bond with the bird or all you will do is scare it. Try read Tips for Bonding and Building Trust

Don't get me wrong there is a chance it will all go fine and they'll get along but it's just as likely that they won't.

30 days is like the very very very risky bare minimum...Most vets says 45 (plus testing) for the safety of all birds..whether or not they seem healthy...they can spread and carry deadly viruses without showing any symptoms for an entire lifetime (while still spreading those to others who do become sick)...cockatiels are especially prone to carrying viruses, but budgies can carry them as well and they can most definitely cross species (regardless of how healthy any of them seem).

They may never get along, and in that case, you must have enough time to devote separate out-of-cage time to each bird...which would end up being like...6 hours if you count the budgies as a pair and the tiel as its' own entity? Make sure you have that time.
As Taiven said, it COULD go swimmingly, but there is SO MUCH to consider and they is no way to be sure they will get along, so in the event that they do not, you must make sure that you have the capacity to handle that (rather than banking on the fact that they will, as there is no promise that it will happen).