The audio forum will have a lot of opinions. I like Audio-Technica and Sennheiser for this, but Rode also makes short shotguns with rechargeable battery power. Your price range will be around 250 and up, with the higher-end shotguns costing as much as your camera, maybe more.
What would help to know is, what you are shooting with this and how you intend to use the shotgun. If you’re for example doing long-distance nature photography and want to capture birdsong, that’s different than putting a directional mic on a pole to grab speech off a person in a news crew interview.
Shotguns are often thought of as specifically for getting a sound from a distance, but really, you should think of them more as a regular mic except with a much higher rejection of unwanted off-axis sounds from the sides. It’s not always the “audio telescope” people think it is.