It sounds like you really want to do a nice job which is great but to be brutally honest with you I dont think youll be able to do that for $1300.00. Because youre planning on getting this on TV you would probably want to use a good 3-chip camera. A decent Sony or Canon camera will run you around $2000.00 to $2300.00. An adequate tripod will be in the $300 to $500s range and from the plan you spelled out, you would need a good wireless mic system which can run between $500.00 and $900.00. A shotgun mic wont work if youre 20 to 30 feet away like you mentioned. Especially by a windy shoreline.
Now Im not sure if youre planning on generating any revenue or not but if you are, maybe look into renting equipment for your first few shows. Once some money starts rolling in, eventually will be able to afford your own equipment which would be more suitable for your needs.