An ATA [Analog Telephone Adaptor] is good for just one type of phone, an old school phone. You will need an RJ11 to BT adapter and depending on the phone itself, you might need one with a ring capacitor.
No idea on the Airband service, you will have to do your research. But a better idea is to find an independent VOIP supplier and migrate phone service to them before you leave BT. That way, when you change ISP, you have no migration of phone service to bother about, Your phones carry on working across the change of isp.
I suggest you sequence this carefully:
1. First, get Airband installed *alongside* your BT service (don't use the one-touch switching service). Also get a VOIP service with a temporary number, and test it works the way you want.
2. Then, port your number to the VOIP provider. This will (or should) automatically terminate the BT broadband as well as the voice; but if for some reason it doesn't, you can terminate it separately.
This approach gives you continuous availability of both your phone number and your broadband.
Regarding the DECT handsets: if you carry mobiles anyway, then another alternative is to use Acrobits Softphone. The advantage of this over most SIP soft clients is that it uses Android and iOS native notifications to wake up the phone to receive calls, so it doesn't drain your battery in the background.
It costs around £7 (or a couple of quid more for Groundwire which adds some extra features like 3-way calling). It's a one-off cost with no ongoing charge, and can be installed multiple times if you have family sharing configured in your app store.
It's been on reduced price of about £4 for the last few days, but that might have ended now.