IVs are run from 0 to 15, and get tacked onto the base values of a particular Pokémon's species; these base values tend to be more than a magnitude greater. Take Vaporeon, for example, with base attack, defense, and stamina values of 186, 168, and 260, respectively. The percent-difference between the stats of the worst and best possible Vaporeon would, thus, be in the single digits.
Furthermore, the truncation of combat power to whole numbers (and the minimum value being set at 10) make the calculation of a low-level Pokémon's IVs a rather more imprecise affair.
Given these considerations, the consensus among most players is that manually checking the IVs of underdeveloped Pokémon is usually not worth it. Your resources (stardust, candy) are typically better devoted to checking Pokémon who are already at a decent level, and of a species that is of particular interest to you (so, like, probably not a Beedrill or whatever).
Level 20 is where it starts to become difficult to gain levels at a rate exceeding one per (long, devoted) day. Also, Pokémon which hatch from eggs (which are noted to have consistently high IVs) are always born with a level no higher than 20. Consequentially, level 20 is the specific breakpoint at which many people say that you should start to seriously evaluate your Pokémon as long-term contenders.
The rarity and power of a Pokémon's species are definite factors in whether raising it from a low level is a good plan or not. Stardust is a commodity, so its value compared to Pokémon with good IVs is inversely proportional to how numerous your alternatives are. Pidgey, for example, is so common that you will almost certainly find a wild, high-level specimen with good IVs. Pidgey are also mediocre enough that such a specimen is only moderately valuable. Dragonite, on the other hand, is one of the finest fighters in the game and rare enough that if I were to find one with perfect IVs I would consider spending the stardust to raise him from any level.
If you have already determined that a Pokémon's IVs are decent and it's a member of a species that you're interested in, there's one last variable to consider before you spend resources on upgrades: its move-set. Most species are attributed, in their final evolution, with a two possible quick attacks and three possible charge attacks, and the difference between an optimal and sub-optimal move-set is far more important than a couple points of IV. The moves that any particular Pokémon will have in its final form are indeterminable until it's actually fully evolved, so, if you have a Pokémon with good IVs that you may be interested in upgrading, first spend the candy to evolve it fully, and then appraise its moves against the pool available to its species. If you find them acceptable, then you may have a serious contender for upgrades!