I'll kick off the thread by sharing my own research and personal experiences, and hope that others will chime in with their own methods and preferences...
First off, just like with any aspect of the automotive hobby, there are often many different ways to achieve a desired goal; and usually, people (men especially) like to argue that "their way" is the best way (go visit the H.A.M.B. forum on jalopyjournal.com sometime and read some of the egos over there- some of those guys are brutal
) I don't really like to argue (however, I do love to debate 
) - so, back to rust - there are many ways to deal with it, and I think each method has certain pros and cons based on:
1) the size of the part being de-rusted
2) the severity of the rust (light surface rust, versus deep, pitting or cancerous rust)
3) the primary agent that is causing the rust (we all know water/moisture is the key ingredient, but there are chemicals that accelerate rust, and then bond to the metal, just waiting to be re-activated again later (IE: road salt, sodium chloride)
The rust treatment methods I have used can be broken down into 4 categories:
1) Mechanical removal - applying sandpaper, abrasives, and good old fashioned elbow grease.
advantages: easy, usually inexpensive (except sandblasting, which requires a sandblaster, or taking the part to a specialty shop). Total rust removal, leaves a rough surface for primers/paints/coatings to adhere to, good exercise
disadvantages: time consuming, sometimes difficult to get into deeper crevices and inside hollow pieces, since it physically removes (strips away) the rust, it may leave pits, pin holes, and other surface defects in the steel, messy (expect to be covered with rust powder, dirt, and blasting media when you're done
Examples: wire brushes, sandpaper, media blasting
2) Chemical removal - using chemicals (typically acidic compounds) to remove the rust
advantages: speedy, most products are inexpensive, parts can be soaked to pull rust from deeper areas and inside hollow parts
disadvantages: caustic, toxic chemical exposure, parts are prone to "flash re-rusting" if not primed, painted or coated right away, many chemicals (as well as road salt) contain chlorine, which bonds to the steel, and is one of the WORST rust activating agents there is, so while you think you are de-rusting the part, you might actually be setting the stage for the rust to come back even worse later on.
Examples: Vinegar, Phosphoric acid, pool acid (the worst option imaginable, BTW, due to the chlorine factor- see above), CLR, Zeps rust remover
3) Chemical conversion via chelation- Using commercial products that "convert" the rust into inert compounds that can then be primed, painted or coated
advantages: ease of use - apply the product, and give it time to do its work, parts can be soaked, allowing rust control inside hollow and deep areas, one of the "old school" favorite chelators (molasses solution) is cheap, enviro-friendly- most chelating compounds are biodegradable and can be poured onto your lawn after use, most chelating compounds will also counter-act any residual chlorine bound to the steel
disadvantages: slow. parts may have to soak for weeks for rust removal to be total and complete, messy, impractical for large parts.
Examples: Eastwood rust converter, Eastwood rust encapsulator, Evapo-Rust, molasses and water (5:1 to 10:1 ratio, water to molasses)
3) Electrolysis - using electrical current to convert the rust within an electrolyte solution (usually washing soda and water)
advantages: "true and complete" rust removal - the reactive rust compound is actually replaced on the part with a dark gray, inert form of iron oxide called hematite (or magnetite) that can be primed, painted, or coated just as native steel, parts are soaked in electrolyte, so the rust treatment is complete inside all hollow and deep contoured areas. enviro friendly - as long as you keep stainless steel out of the electrolyte, it can be disposed of by pouring onto your lawn (stainless steel contains chromium, and in the presence of electrolysis , this will create toxic chromate compounds that are very dangerous- if your electrolyte turns yellow, then DON'T dispose of it by pouring it onto the ground). lower risk of re-rusting due to inert iron oxide coating, attacks any residual chlorine ions that are bonded to the steel for a longer term rust-proof part
disadvantgaes: requires specialty equipment; although the method I have used with success, (and is greatly detailed in the link I provided below) can be set up with a plastic container, a battery charger, and some sacrificial steel rods or rebar, impractical for large parts (like frames and body panels)
Here are some great links for reading more about Electrolysis and Chelation methods:
Electrolysis: http://1bad6t.com/rust_removal.html
Chelation: http://www.worldradiomagazine.com/old_wro/articles/columns/wp0906/wp0906.html
So, now that you've chosen and applied whatever method you are going to use to remove (or convert) the rust, what to do next...? How do you keep the part protected to prevent the rust from coming back?
Again, there are as many options as there are opinions about which option is best, so I'm going to share my viewpoints, without making any claims that any of my preferences are "the best way" - just like with rust treatment and removal, I think each option has pros and cons, and therefore it comes down to personal choice.
When the rust removal process has left a nice, rough surface with "bite" (especially after media blasting or manual sanding) my personal favorite next step would be the application of an epoxy based primer (like PPG DP series primers)- the primer dries flat, and can be top-coated in any color with many commercial paints (urethanes and enamels)
If you used a rust converter product, or used the electrolysis method, then your part will already have a nice flat black oxide finish that can be primed, or painted directly.
It is also possible to combine several processes together, as I did on the frame of my 65 hardtop- I stripped the rusty frame down with a wire wheel, smoothed some rough areas with a sanding disk, and then coated the frame with Eastwood Rust Converter to take care of all the residual rust that was left by the wire wheel and sandpaper. On top of the Rust Converter, I will paint the chassis with several coats of gloss black Rustoleum enamel, which has been a 20+ year favorite topcoat of mine for chassis components.
Another commonly used product is POR15 chassis black coating. I know a lot of folks swear by this product, but I have found the following 3 tradeoffs to be personally undesirable:
1) POR15, like epoxy primer, really likes a rough surface to "bite" - I have had issues with POR15 lifting after a couple years, when applied over smoother surface finishes
2) POR15 is thick- if you leave any components bolted to the frame when you paint it, the POR15 "seals" the bolt heads in place, and when/if you go to remove the bolts later, they chip the finish, which again opens the door to the risk of the finish flaking off.
3) POR15 is about 4x more expensive than Rustoleum
Again, I don't mean to be offending anyone- if you use and love POR15, then I am perfectly cool with that
One last important point to consider with regards to rust is the vehicle's "living environment" - down where I am in the arid southwest, cars don't rust naturally- you have to really work at getting the rust started
and so- There are certain aspects of these rust treatment methods that may be more than adequate for down here, but would be totally inefficient up in New England.
Don't hate me Justin... 
