pronunciation - TH sound, is it continuant or stop?

How do you all pronounce the TH sound when speaking fast?

For example, I've learned to pronounce the TH sound like a continuant sound, for example the hard one: ð. I start doing a Z, so this Z go between the the teeth and creates the TH sound. Like a lisp (definition by Macmillan).

But when I speak very fast, the sound becomes like-stop way. That sounds to me like a big difference, it's so different like a "SH" (continuous) and a "CH" (stop).

When I hear native speakers, most of the time their TH sound sounds like a D did behind the upper teeth; I think this Wikipedia did call "Dental Approximant".

But is very confusing to me, because they're three differents sounds, the TH continuant, the TH stop and the TH approximant.

I would really like to pronounce the continuant one, but sometimes it's impossible, sometimes I just stay silent when I don't know what sounds right and natural.
For example when I say, "The Rules" I might use the approximant or the stop, just for shame.

According to Wikipedia, ð is continuous and the others are variations.

I saw people just doing a T or a D between their teeth.
But, this sound more different yet, because I can do a N, L the same way, so this T/D are just T/D in different places.

I saw that sometimes people pronounce approximants on TH beginning words, and continuants on the middle of words.

Are these variations natural, how do you do your TH?
What is considered normal? How do you learn it at school?
Is it impossible to run away from these variations?
Does it sound weird if I say "THen" like "ZHen", the ZH represents a "Z lisp"?

P.S: the unvoiced TH shows these variations:
Continuant is S with a lisp, stop S with lisp and the T dental approximant.

http://en.wikipedia.org/wiki/Voiced_dental_fricative
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2981115/

Sorry for the errors, I've stopped studying grammar because I just need to learn this first.

Answer

In standard English, 'th' is always a dental fricative, a non-stopping, continuous movement of air between the tip of the tongue right and the bottom of the top teeth. It is almost exactly the lisp sound.

It is a rare sound in the world's languages, so most language leaners of English have trouble pronouncing it and attempt to approximate it by the fricatives s/z or the stop t/d.

There are some non-standard varieties of English that use t/d naturally instead of the fricative, like for example Sylvester Stallone in Rocky, or any number of street-wise New Yorkers. So don't emulate this unless you want to sound very urban (and a bit out-of-date)

As with most phonetic things, learning it comes with practice and listening and more practice. For 'th' in particular, a little bit of your tongue sticks past the top teeth, so may feel weird (or even rude depending on your culture).