Water isn't going in the outflow...
Even though we landed on the moon and are able to comunicate freely across the globe in real time, we still are sometimes stumped by mundane things like clogged pipes - what do we do then, in our hi-tech, modern times?
The same thing as always - call in the plumber. There maybe quicker and cheaper solutions, of course - but unless you are sure that drain cleaner isn't going to melt your pipes, or actually just do what it is supposed to, it is better to leave it to professionals.
There are some things, in the pipes, that you don't want to see - trust me on that. Besides, expert plumber can always recommend what to do, to avoid this kind of situation, and which products to use if need be.
Other than that, it usually takes something more sophisticated than a plunger, to get rid of the clog - if you even have that to begin with. So don't fret, or take this as an insult to your aptitude, and contact with plumbing services.
Different pipes for different purposes
Constructing your plumbing and drainage installation, isn't as straightforward as it may seem. First thing you need to choose, is what type of pipes are you going to use? There is plenty to choose from, but not all are multi purpose and good for your home.
Generally speaking, you need the ones relatively easy to install, repair if needed and with long life span. Price is also relevant, of course, but sometimes it is better to pay up more up front, rather than upgrade it later.
The answer to such problem is only one - PEX pipes. You might thought that copper pipes are better, but they aren't - harder to install and much more expensive. All in all, pipes from PEX are very good, either for the plumber or user. The only thing that's left, is to find were you can get them cheapest, and in required diameters.
Wikipedia about the history of the plumbers
Quick look in to the history of the plumbers, thanks to Wikipedia:
The word "plumber" dates from the Roman Empire. The Latin for lead is plumbum. Roman roofs used lead in conduits and drain pipes and some were also covered with lead, lead was also used for piping and for making baths. In medieval times anyone who worked with lead was referred to as a plumber as can be seen from an extract of workmen fixing a roof in Westminster Palace and were referred to as plumbers "To Gilbert de Westminster, plumber, working about the roof of the pantry of the little hall, covering it with lead, and about various defects in the roof of the little hall". Thus a person with expertise in working with lead was first known as a Plumbarius which was later shortened to plumber.