The old API-650 used a single, somewhat low, allowable stress for all applicable steels. At some point, they added an appendix that allowed higher stresses with increased inspection and othe requirements. In time, that appendix became the main design method, and the original design method was moved to Appendix A.
Appendix A is supposed to only be used when specified by the owner, but most owners will let you use it if you propose it. Appendix A will let you use A36 steel where you might not otherwise be able to. And it will let you delete radiography for some tanks if you owner will go for it. Appendix A is not just a different way of calculating shell thickness, it includes a number of other changes to the base code. Appendix A actually does use the one-foot method for shell design, but uses different allowable stresses and different joint efficiency.
If you use the base code, you have a choice of the one-foot method or the variable design point method (or shell analysis theory). If you're new to the standard, just use the one-foot method and be done with it. The other methods allow somewhat thinner steel on larger tanks.
General steps involved in design of an API-650 tank are (with some variation):
-Check lowest design temperature and select acceptable steels
-Design shell for product and hydrotest conditions using one-foot or VDP methods
-Check shell for blow-in, and increase shell thickness or add intermediate wind girders if required.
-Design wind girder if open top or roof if fixed roof
-Check for wind overturn
-Design for internal pressure by Appendix F if applicable.
-Check for seismic stability by Appendix E.
-Size vents per API-650 and API-2000.
If you're new to the standard, take a bit of time and thumb through it. Most of the design for a normal tank is in sections 1-3. Get familiar with the appendices so you know when to refer to them. You will need structural design codes (AISC-ASD or equivalent) to design roof structure.
AISI has some guides on steel tank design, thought they are somewhat dated. AWWA has a manual on steel tank work, although oriented towards water tanks.