TIFF
TIFF is a lossless file format that can hold a lot of image data and layers. It's used for archive, print and as an intermediate step between Lightroom and Photoshop. Unlike JPEG, TIFF loses no quality when you resave it.
When you send a photo from Lightroom to Photoshop, it often goes as a 16-bit TIFF, so you keep all editing room and any layers. TIFF files are large, so use them for working files and print, not for the web. For the end user you then export a JPEG. Feel free to keep important edits as TIFF when you no longer need layers but still want top quality.
Read also the in-depth explanation: TIFF explained.
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The presets on this site set these adjustments up for you as a starting point, which you then fine-tune to taste.