Unicode Variation Sequences have to be defined as part of the Unicode Standard, you can’t just use Variation Selector characters to affect private substitutions. There are a number of math operator characters that have defined Variation Sequences, but this is not used for super- or subscript characters,
Apart from the handful of characters that have encoded super- or subscript forms in Unicode, there are two clean ways to obtain these in Unicode text using OpenType fonts. One is to use the or OpenType Layout features in any simple text environment with OTL support and with, of course, an appropriate font that contains the super- and subscript glyph variants that you want. This has the benefit that it works in most modern text environments with relatively little effort, and if you are only doing simple inline equations with single level of un-nested -script variants, this would be fine.
Things get more complicated if you are doing more complex equations, or need nested and multilevel -script variants. Then you need both an environment and a font that supports math layout. In such fonts, the -script variants are not pre-scaled and aligned as in simple OT fonts, but instead they are optical size design glyphs included in the font that are then dynamically scaled and positioned by the math layout handler. The font MATH table contains information for default scaling and vertical alignment, but the math handler also contains intelligence to adjust size and height further in some situations. The font may contain two different sets of optical size glyphs, so one can apply -script variants to -script variants for nested and multiple levels.
For more information on OT math fonts, see the Mathematical Typesetting book that we wrote for Microsoft.
In terms of input, I suggest looking at the conventions used in TeX or in MS Word, which have fairly intuitive input methods for equations.