One question is the structural integrity of the tank. If it's in danger of failure then spray-on liners and similar fixes won't do any good.
One question is, are there any regulatory requirements for inspection and repair of the tank. In the US, you may have federal or state regulations requiring tanks to be periodically inspected and/or maintained in accordance with API-653. If you're not in the US, that may not be the case, but any such requirements would need to be confirmed prior to doing any work.
Replacing the bottom and first ring of shell on a tank is a sizeable undertaking already. Prior to doing that, I would certainly look very closely at the cost of replacing it with a new tank. The new tank would be far preferable, even if the cost were comparable.
One thing I recall hearing from a certain old-timer was that doing any welding on a riveted tank could cause existing joints to start leaking that were not leaking before, and seal-welding those could cause other joints farther down to leak, etc. Another thing I recall hearing is that riveted tanks were not necessarily made with "weldable" steel, and welding could be more difficult because of that.