Only the portion of the amount rolled over from the 403(b) to the Roth IRA that represents your original contributions to the Roth 403(b) become contribution basis in the Roth IRA. This amount will be reported in box 5 of the code H 2019 Form 1099-R that you will receive reporting the rollover. Until you receive that form in early 2020 you'll need to look at your 403(b) transaction history or code BB amounts from past Forms W-2 to find your Roth 401(k) contribution basis that became Roth IRA contribution basis as a result of the rollover.
Because you made $30,000 of regular contributions to the Roth IRA, you'll certainly be able to obtain a distribution of $30,000 from the Roth IRA tax free as you stated. Whatever additional amount that you be able to distribute from the Roth IRA without any consideration of what the funds are used for will depend on the amount of contribution basis rolled over from the Roth 403(b). Beyond that, if you qualify as a first-home purchase you'll be able to take out $10,000 of earnings tax and penalty free.
