Refinishing Painted Porch Railings: Balustrades: Give New Life to Old Porch Railings

My husband and I are the proud owners of one of only three Sears Honor Built Magnolias known to exist in the United States. The house was offered by catalog from 1918 to 1921.  It is located in Piedmont, Alabama and is subject to all the harsh weather the South has to offer.

The front porch was surrounded by a once beautiful balustrade, as were several other locations on the roof lines of the house. I say once, because when we bought the house, the front porch balustrade was falling apart, so we took the rest of it down and now have it inside the house and out of the elements.  I am now in the process of sanding each balustrade down to the bare wood and removing almost 90 years of paint.

What are the best products to use for refinishing the balustrade? In which order and manner should the products be applied to the balustrade to gain the best result and allow for the longest period of time between having to go through this entire refinishing process again?

The Money Pit Answer

It sounds like you own a home that is truly a part of home improvement history!  Thanks to the availability of rail service that covered most of the United States by the early 1900's, catalog houses were an economic reality.  Sears initially sold only house plans by catalog but in 1911, they expanded that service to include the house itself.  Over the 20 years or so that I spent working as a professional home inspector, I had the opportunity to inspect many of these homes and I can tell you that they were extremely well built.  I am happy to offer some tips to help you restore yours to its former glory.
First, a note of caution:  You mentioned that you had taken the balustrade down and moved it inside to work on stripping the paint.  As you may be aware, old homes are chock full of lead paint.  By sanding off the paint from the balustrade in the house, you may very well be exposing yourself and your family to a toxic condition.  So, please cease doing any of this work inside your home!  Any work removing the old paint should be done outside with proper precautions. 
For more information on lead paint hazards see the EPA's lead paint website.
Now, on to refinishing the balustrade!  The products you choose will depend on the finish you would like to achieve. 
If you want to replace the rich full color of the original balustrade, I would recommend a solid color stain.  The Flood Company, who has been making finishes since before your house was born, makes a product I like very much called CWF-UltraLast Premium Solid Color Finish.  It is specifically designed as a reliable problem solver for re-coating old applications and is the only solid color finish that does not require a prime coat.
The finishes consist of an oil-based primer and acrylic/urethane finish in one.  As a result, the finish not only lasts longer, but is far quicker to apply.  It also cleans up with just soap and water.  Considering all the hard work you are putting into getting the old paint off the balustrade, I'm sure you won't mind saving a step or two on the refinishing process.
CWF-UltraLast is available in 60 colors and is guaranteed not to peel or blister for 15 years on siding.  Properly applied, I'm sure it will last at least that long on your painted porch balustrade. I have used various CWF finishes over the years for siding, fences and decks and have always been very happy with the result.