Ok, here it goes.
Depending on the design, you should have a black on white only version if possible - so called sillhouette version. If not doable due to whatever reason ask for a test of how your logo looks on white and dark backgrounds and if needed ask for a separate colour version for dark backgrounds.
Your logo can have various ‘locks’ or compositions. Y’know, mark left logotype right, mark big on top with small logotype bellow, mark only and so on. Agree on these beforehand. Less is always better, but it really depends on where the logo will be used and reproduced. Once you have, let’s say two locks agreed and designed - each of these locks should be delivered in RGB and CMYK colours (possibly Spot or PANTONE if you’ll be using that print method) and in two different bitmap and vector formats. Vectors are scaleable so just one RGB and CMYK Illustrator .ai file + one .eps. Oh and vectors need to be outlined - ie no fonts left editable (that you may not have or the printer) only curves. Bitmaps will need to go in three sizes for each lock + favicons separately and can really only be in RGB. If you’ll be printing your logo always send vector files anyway - so your bitmaps are for web really. So each lock in three dimensions in both .png transparent and in .jpeg.
So: however many locks > vector RGB and CMYK in .ai and .eps + small, medium, large .png + .jpeg
Repeat for all colour variations and sillhouette version.
Favicons are their own thing, should get them separately and ask for few colour versions (so you can test which works on both light and dark browser windows).