Just about any shotgun mic out there is gonna run less than or very close to $350 for what you are looking to use........Azden is probably the cheapest and thier SGM X2 is a good option (around $250 I believe) Rode makes a good one as well Ntg 2,but I don't care for the suspension mount it uses (too big), Sienhiesser is probably the best in quality and performance the ME 66 is a reasonable choice @ $360.00.

Whatever you chose I would recommend an XLR style output (or balanced output cable) A mic that uses it's own power source as opposed to phantom power and something with a good suspension mount for isolating it from the camera (won't p/u motor noise) and get a good aftermarket wind muff for it.

Good luck!