quarterly taxes

You had several questions:

Does she need to file quarterly taxes and if so, how much or how do I calculate it?  

You can use either the IRS calculator, or one included in TurboTax

Tax Withholding Estimator | Internal Revenue Service (irs.gov)

To calculate your estimated tax payments for 2020 please follow these steps:

1. Sign in to your return.
2. In your return, click Federal Taxes > Other Tax Situations.
3. In the Other Tax Forms section click the Start/Update box next to Form W-4 and estimated taxes.
4. On the screen, Adjust How Much Tax You Pay, click the No box. [This for withholding from your paycheck.]
5. On the Review Your Estimates screen, click the Review Now box.
6. You can continue through the screens and review your entries.

Does she need to pay Medicare and SS taxes regardless? 

Yes, this is refereed to as Self-Employment tax, and it comes to 15.3% of gross profits from a business.  Provided you enter the estimator correctly, it will include this in the estimated payments.

How do I calculate that? 

As stated above, you do not have to.  The estimators will take care of it.

What turbo tax will we require moving forward

You will need the Online Self-Employed, or the Desktop Home & business

Either will work.  The Desktop has more features.