There is extremely little setup involved in any apple airport.
But we have no idea of the current setup.. continual cutouts sounds like a wireless issue.
Plug the Mac into the TC by ethernet and see if that improves things.
Otherwise post a lot more details of the network.
1. What modem .. make and model? What role does it have if it is a full router.. is it bridged or indeed running full router.
2. How is the TC connected and running in what mode?
3. Are there any errors showing in the TC setup?
4. What wireless speed and internet speeds are you getting? Is it comparable to what the R6300 managed?
One simple fix.. put the R6300 back in the network.. bridge the TC and plug it into the Netgear and use that for your TM backups and wireless if it works ok.