Is it worth to buy cheap used LP special 2 and than replace pickups and tuners or is it better to buy better guitar? How much does good pickups for this guitar cost?
Better guitar, easily. The Special II serve their purpose for new players, but I wouldn't like past them for anything other than that.

What's your budget for a guitar? Are you willing to look used? And where in the world are you located?
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Definitely a better guitar. Changing pickups etc should be the absolute last thing you do to fine tune your tone once you have a decent quality setup.
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And before a better guitar, consider a better amp.

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Don't buy that guitar. Get a Squier CV or a Epiphone LP Standard.

You do need an amp too, don't be cheap, get something decent.
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Sure upgrading your gear will make you sound better.

Yeah, if you plan on changing pickups you should be looking at the Standard models at the very least, I wouldn't want anything less than a Custom as far as the Epi's go...

Or, depending on the budget, look at the Tribute models, or an actual Gibson LPJ... Those models already have great pickups.