A Base Rare Monster is a classification of monster that, at its lowest level of evolution (officially the Stage 1 form), are Rare Monsters.
Base Rare Monsters on this wiki are categorized such that while a Spry is an Epic Monster itself, and Viraconda is an Ultra Monster, both are Base Rare Monsters since their Stage 1 forms, (Spug and Venoper respectively) are Rare.
Most Base Rare Monsters evolve into Epic Monsters in their 2nd form, and Ultra Monsters in their 3rd and final form, although there are exceptions to this rule, like Aurora and a few others.
A list of Base Rare Monsters can be found on their category page here.