Tiffs are uncompressed image files. Therefore no way of reducing the file size in export from LR.
For web use, normally always use Jpegs. For normal web use, a maximum file size of, say 250Kb will be adequate and for some of smaller dimensions you may find that 30Kb is more than enough. To some extent it depends upon the range of colours and the amount of detail in the original file.
As has been mentioned above, simply opening and closing the web pages upon which the Jpegs appear does not, in any way, degrade the image quality.