Could/will evolution eventually lead to a single "perfect" self sustaining species

This is obviously unanswerable, so I'm really asking more for educated opinions on the matter.
what classification would the species likely belong -or be closest- to (kingdom, phylum, class, order, family, genus)?

Well, it's difficult to get into any specifics at all for this question since we would need to define everything from the exact definition of "perfect" to what is meant by "self - sustaining".

In a strict sense, there could never be a self - sustaining organism that perpetuates itself for all time because it will always rely on input of energy from the outside environment (that is, unless it can somehow thwart the second law of thermodynamics), and however long it takes, the outside energy sources such as the sun, or stars for any other life that may be out there in the universe, will one day be gone by some means or another. To view it in terms of entropy, the very existence of life goes against the favorable tendencies of chemical reactions in the universe; life is about order, organization, a decrease in entropy, while the universe tends towards increasing entropy and chaos. In the end, the universe will come out as the inevitable victor and eliminate even the most efficient organism.

To address the matter of perfection, I am inclined to think that there never will be a "perfect" species or even really a "close to perfect" species of any sort produced by evolution. This is because evolution is not actually a conscious process that sets out to fashion perfection in life. Rather, it describes how animals that are more reproductively fit tend to contribute more to the gene pool (this is called natural selection), and thus their genes, over lengthy periods of time, become more prevalent in the population. The variation in traits is introduced by random mutations, and differing trends in the environment tend to favor certain traits.

Note that the process of evolution, strictly speaking, favors reproductive fitness, that is, ability to pass down one's genes. This does not necessarily coincide with any definition of perfection. For example, let's say males of a bird species tended to mate much more successfully if they have wild, showy colors on their feathers that stand out very easily. Even if this makes them more vulnerable to predators, this trait very well may be propagated despite being very detrimental to the lifespan of the males of the species.