The answer is paradoxical – a NON-NATIVE speaker! It is true that the perfect pronunciation, the right stress, the melody of voice, the nice fluency and the rich vocabulary... we can find usually in the speech of a native speaker. But keep in mind that the majority of users of English language in this world today are non-natives. You are also one of them (probably). The English we are learning is intended to be the mean of communication. You will use is with both natives and not-natives.
I found in some stage of my English journey (and my friends confirmed me my experience too) that in many cases is the listening to somebody who was not born in English speaking country quite demanding. In some cases more difficult than listening to any native Englishman or American or Australian. Sometimes it could be quite a challenge. We, language learners, usually complain that the natives talk too quickly. In my opinion it is not the biggest problem. Maybe the bigger is the slang and idioms. Of course, the listening needs some practice (like everything).
My point is that the listening to a non-native speaker could be a good practice, a good valuable exercise. Of course that the bulk of your study should be based on a “proper” English, especially in the beginning of your journey. But after while you do it I would suggest to incorporate non-natives too. I remember myself when I started to listen Osho for example. It was really a challenge for me. Fortunately there were transcripts available. After while I accustomed to his pronunciation, voice, vocabulary. By the way his vocabulary is quite rich. It is true that he does (maybe I should say DID – he passed away a long time ago) some mistakes while speaking. But is it a problem? Definitely not for him. Maybe even we, who are learning English, can gain from that - noticing them a learning from these errors. On the other hand, I would be careful to listen such materials too early. There is a possibility to learn this incorrect English (we usually do at school from our school mates anyway) By the way not to forgot to read my disclaimer :)
There is a lot interesting people on this planet and you can speak (read or write) with nearly all of them in English, there is a lot of materials in English available today. Some of them were created by not-native speakers and are worthy to listen or read (e.g. this blog :-) LOL)
One of another such people I like to listen is Deepak Chopra (born in India) Enjoy this short video (extract from Deepak Chopra - How to know God)
Around 1890 chief Crowfoot a Blackfoot Indian was dying
and he whispered into the ear of a missionary father:
What is life?
It is the flash of a firefly in the night.
It is the breath of a buffalo in the winter time.
It is the little shadow that runs across the grass and loses itself in the sunset.
Life as we know it flickers out all too fast In death we return to the light, the source where we all began
Then, all of reality has only one source
You are that source
God is our highest instinct to know ourselves.
The Persian mystic poet Rumi once said,
When I die I will soar with the angels,
And when I die to the angels,
What I shall become you cannot imagine.