Remove the silicone first. Nothing else will stick to it, including silicone itself. There's this great product out there called McKanica Silicone Caulk Remover. You can get it at most hardware stores. Use that to remove it, then clean the surface with rubbing alcohol to ensure the surface is super clean and free of silicone.
A couple other things: if there is mildew in the silicone, that is sometimes a sign that there is moisture getting behind the bead and growing underneath the caulk. In a shower like you have, weigh down the floor with something heavy (a 5-gallon bucket of water will do) to help "expand" the joint so it's at its widest when you apply the caulk. Leave the bucket in there until the caulk has dried a bit, say 4-8 hours. That will help ensure your caulk bead won't get stressed as soon as someone steps in the shower.
I would recommend you use a caulk that has a guarantee to be mildew-free for several years. There are several out there. Do some research and I'm sure you'll find something that will work great.
Hope that helps!
-- Charis w/ Sashco - www.sashco.com