Under what status would I file if I indicate that I can still be claimed dependent by someone else? I will be filing for the tax returns.

Your filing status is Single.   In My Info you will have a question that asks if you can be claimed as someone else's dependent.  Your answer needs to be YES.

CAN I FILE A RETURN IF I AM A DEPENDENT?

If you can be claimed as a dependent on your parents’ return, you can still file your own return so that you can receive a refund of taxes withheld.  Your W-2 will show federal tax withheld in box 2, and state tax withheld in box 17.  (You will not get back anything for Social Security or Medicare withheld.) Be sure that on your own return you say that you can be claimed as a dependent on someone else’s return.

https://ttlc.intuit.com/community/children-dependents/help/do-i-need-to-file-my-own-taxes-if-i-m-a-dependent/00/26111

If you can be claimed as a dependent and you answer the question in My Info incorrectly, here is what happens if you e-file first:  Your Social Security number goes into the IRS system as having been used.  When your parents try to e-file, their e-file is rejected and they will find it impossible to e-file their own tax return.  Then they will have to print, sign and mail their return and wait for months for it to be processed.  You, meanwhile, will have to file an amended tax return on a special form called a 1040X, which also takes months for the IRS to process.  So make sure you know the correct answer to "Can anyone claim you as a dependent on their tax return?"