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Since I left MN have not brewed, I was spoiled by the great suppliers there, Midwest supplies and as Griffin said Great Northern. I specialized in Ales only, specifically IPA's. I did Liquid Malt extract brewing with a partial mash to keep it simple yet still able to make some amazing brews. I just felt is was easier than whole grain brewing yet gave me close to the same flavor profiles.
The propane burner would work well. I suggest a 5 gallon minimum stainless kettle to brew, 6 gallon would be better so you could boil almost the full 5 gallon batch. Get two glass carboys both 6 gallon one for initial ferment and the other which could be a 5 gallon for the secondary ferment. I used a large diameter blow off hose for the primary fermentation which ran from carboy to a sterile bucket with water in during the initial ferment stage. A rubber cork with hole for a airlock is needed for secondary ferment. Get a large size funnel for moving from brew kettle to ferment carboy is helpful.
I highly recommend a auto siphon for moving beer from primary to secondary ferment and from secondary ferment to bottling bucket (plastic okay here). Msc tubing to run from bottling bucket to a bottle filler to fill bottles. A bottle drying tree not bad idea. A ferment thief ? a device to take some liquid from a carboy to test specific gravity which you will also need. Miscellaneous cheese cloth bags for mashing the grains and even adding hops to keeps some of the hop crap out of the brew kettle. Large kettle size stirer. Bottle capper (hand held is okay), sterilizing chemicals. That is most of what you need. I fermented in the basement of our house which rarely got much over 78 even in hot summer. Winter was perfect where it would stay in the 60's.
Sure I forgot some stuff but thats a pretty good list. Not sure if there are any brew supplies stores around you in GA. I lived close to midwest and would drive there, I was spoiled. Their grain room is bigger than most brew stores down south.
Good luck, patience and keep everything sterile I cannot emphasize sterile enough. Would hate to have a batch go 6 weeks before tasting only to find it ruined.