Obviously you haven't read enough. I've been brewing all grain for two years now with no mash tun at all. Search for the term BIAB. You don't have to use that method but you should be aware of what it entails.
With all due respect, you still have a mash tun. This is nothing more than a container that you mash in. The mash tun could be combined with a lauter tun, in which case it is usually described as a mash lauter tun, it could be a completely separate vessel, or it could be the brew kettle.
BIAB eliminates the need for a false bottom, manifold, or braid, but you still need a mash tun to contain the bag, even if it is your kettle.
In response to the OP, a false bottom or a properly designed manifold is probably best if you fly sparge.
If you batch sparge, there should be very little (if any) difference between manifold, braid, or false bottom.
If you brew in a bag, the bag replaces the manifold, braid, or false bottom, but you could have conversion problems if your water is excessively alkaline.
-a.