That's a c-melody saxophone, between alto and tenor in range and keyed to concert C.  C-melody saxophones were marketed towards amateur players who wanted to read off the same music sheets piano players use.  They have been out of vogue for a number of years, but they have been used in some recent recordings.  

There are a lot of factors that would figure into how much you would want to spend on repairs.  If you were considering selling it, the cost of a full repad could easily exceed the market value of the horn because c-melody saxophones are a rather small niche market.  But if you just want to get that beautiful horn in playing condition for you and your family to enjoy, it's easier to justify the cost of repairs.  There's no substitute for having the horn inspected to get an estimate of what it would take to restore it to playing condition.  If there's corrosion affecting the springs, rods, and pivot screws it could drive the cost up considerably.