The least expensive option for eliminating reflection is to avoid the use of any glazing (glass or acrylic) in the picture frame. The obvious advantage of this is lower cost because you eliminate the glazing. Unfortunately, this option has serious drawbacks in that the artwork has no protection from curious fingers and atmospheric pollutants. It also results in less protection from UV radiation. And If the artwork itself is glossy, you will still have reflections with improper lighting.
Assuming you are going to use glazing, the next least expensive option is to combine regular glazing, meaning glazing without any built-in reflection control, with proper lighting. Gallery lighting is accomplished by placing the lighting directly above the artwork and fairly close to it. This results in the light hitting the artwork at a steep angle so you only see reflections if you are below the artwork looking up at it.
If you can not control the lighting the next option is non-glare glass or acrylic. This type of glazing has an etched surface on one side that helps reduce the reflection. The disadvantage is increased cost and a slight loss of sharpness. The loss of sharpness is proportional to the distance between the artwork and the glazing, which means that this option will not work for shadow box framing.
The final and most expensive option is the use of anti-reflection glazing such as Tru-Vue Museum glass or Optium acrylic. These types of glazing have a special coating that helps reduce reflection without causing any loss of sharpness. This option provides your artwork the full protection of glazing with the look of having no glazing at all.