There are two major groups those that arise in hot springs and those from composting systems.
Hot spring microbes are chemotrophs using oxidisable inorganic energy sources, they are also usually tolerant of high acidic.
The composting microbes grow on complex polymeric substrates and their monomers.
The media should be like the environment that the organisms would normally grow in. The contaminating microbes will not be able to compete under these extreme conditions.
Which general type you are after will determine the culture conditions, it will need to be liquid media, because Agar will melt or be very soft. I'm not sure there are other solid media - speak to Oxoid or other media suppliers, there are also a number of research institutions that work with these organisms all the time.
Halophilic medium modified from the formulation of Oren (1983) was used, comprising (per litre distilled water): 125 g NaCl ; 100 g MgCl2.6H2O ; 5 g K2SO4 ; 0.1 g CaCl2.2H2O ; 1 g yeast extract ; 1 g Casamino acids and 2 g soluble starch. The pH was adjusted to 7 and incubation was at 37oC.
Oren, A. (1983). Halobacterium sodomense sp. nov., a Dead Sea halobacterium with an extremely high magnesium requirement. Int J Syst Bacteriol 33, 381–386.