Did some work at at place with various Anechoeic chambers, they looked really cool, like something from Sonic the Hedgehog.
Bit more advanced than egg boxes and curtains... bit more expensive too I reckon
Depends on the area that needs treatment and also on what you want to achieve.
I suspect you are faced with two challenges - keeping the recording area isolated from outside sounds (family, home working by others, ice cream van and such like) and also reducing reverberation etc within the booth that might otherwise affect the quality of the recording.
We use Tecsound 100 as a barrier - dense at 8kg/m2 and can be supplied as self-adhesive to go directly on walls. The other good product from CMS Danskin is a combination of a high density felted product (two layers) wrapped around a centre core of Tecsound. This can be put into a frame to both reduce reverberation and to isolate you from the outside world.
Think about soft covering on the floor and don’t forget the ceiling... you can get dense fabric baffles that will reduce echo etc.