Replacing old well tank that is leaking
Yes, your plan is a good one.  I'd remove all that cast iron pipe that I could and replace it with copper.  Be sure to use a dielectric union on the iron/copper connection to avoid corrosion problems.
You'll find that a newer bladder-type tank will not waterlog the way the old air over water ones did.  Be sure, however, that the tank is not in a location that freezes.  Ice in the tank will rupture the bladder.