I would assume that your brew pot has a ball valve attached for draining? That's really the only way you would want to use a false bottom as that acts as a filter when draining your mash tun. I personally would not recommend using a false bottom when boiling due to the possibility of scorching. A bazooka screen would be fine I would imagine and may help "filter" your wort before going into the fermenter, but that is definately not required by any means.
Personally, I would just hold off on using those until you start getting into AG brews.