During my trip in China I wouldn't like to carry all my gifts in my bag, so I'm planning to send them by post. Where is the best place I could do this with minimum problems? I'm planning to send it in the cheapest way possible. I will visit most big cities like Beijing, Xi'an, HK and others. Should I pay any taxes when I will receive the package?
Most any post office can send a parcel for you, but the cheapest method would be sea mail, which will take a fairly long time to reach your home address (possibly a couple of months).
Duty that might be due upon receipt of the package will depend on where you live, as each country has different rules, and what exactly you are sending. Most countries allow a reasonable amount of personal items to be sent duty free, but the limits depend on what it is. Jewelery is much more controlled than say t-shirts, high tech electronics more limited than handicrafts, etc. Your best source for information would be the customs website for your country.
If you go to the local post office, you should be able to get all the infos you need. I travelled to china some years ago and staid there for 3 months, basically I had the same problem. I just went to a post office and asked for infos.
Assuming “Europe” means EU, sending by post instead of carrying things in your luggage does have drawbacks as far as taxes and duties are concerned.
Travelling by air, you have a €430 duty and VAT-free allowance. For things sent by post, the threshold for import duties is €150. VAT depends on the country but might need to be paid even for postal consignment with very small value. This also means that even if the goods you want to send are very cheap and intended for your personal use, you still need to do some paperwork in advance (which is not the case if you carry them with you).
That's not to say you will definitely get in trouble if you try to cheat, but those are the rules.