So your plan is to lay the 1/4" sheet over the cracked bottom, correct?
For the silicone, you don't want to use anything from HD/Lowes or a fish store. You want to use G&E SCS1200 series, Momentive RTV100 series, or another quality adhesive silicone. You could probably get away with a regular sealant type silicone, but if it were me I would definitely want to use a proper adhesive silicone. You can order the momentive from mcmaster and it will arrive in just a couple of days.
Also keep in mind that this will need to cure substantially more than the 24 hours that it says on most silicone tubes.