As far as I know, it doesn't really matter as long as it's vented outside. Venting into the attic is Very Bad -- in the winter, the humid air will condense and (if cold enough) freeze, and you'll effectively have water in the attic.
For any vents, the straighter the run is, the more efficient and quieter it is. Avoid corrugated pipes, and avoid bends and elbows as much as possible. For that reason, going into the soffit almost guarantees you'll have more bends than going through the roof.
- As an aside, I have two bathrooms, and they both have the identical fan (which is rated as very quiet). One bathroom has a 3" duct that is about 3' long, and goes almost straight out the side of the house (it's done with a small section of flex line that bends up and over be a couple inches, because I lined up the vent on the outside with the siding). The other bathroom vent has a 4" x ~6' line that has two sweeping turns and goes out the side of the house. The second one is noticeably noisier than the first.
As a DIY job, you'll also have to be sure you have the knowledge to cut a hole in the roof. I'd say it'd be far better to go out the side of the house (which is a bit easier to seal) than to go through the roof and cause a leak.
Much too much up and down! You want a P trap with an additional angled connector toward the wall.
The first down and up from the sink drain is correct. That is the P trap. It should end with a horizontal leg pointing toward the wall (an L shaped piece).
![ptrap](https://i.stack.imgur.com/aKQbU.jpg)
This will not line up with the opening in the wall because the drain is offset. Therefor that leg will run a distance and then will use an angle to bend it back toward the wall.
You could use a right angled slip joint connector (running horizontally).
![slip elbow 90](https://i.stack.imgur.com/NN4GB.jpg)
A 45 degree angle would be better (the less sharp the bend, the less likely to stop up). However it may be hard to fine a 45 degree slip joint elbow. You could use standard pipes and elbows, but these would require glued joints rather than slip joints.
Finally there should be a straight run from the angled connector to the wall connection.
You can rotate the P part of the trap so the L leg coming off the P is parallel to the wall (assuming you are using the 90 degree elbow; if not, adjust accordingly). Then the elbow turns the drain toward the wall. Another horizontal run carries the drain back to the wall.
You need to measure the length of the horizontal leg of the P and the length of the connecting run to the wall; be sure to allow for the sections embedded in the elbow and trim each accordingly. Assemble.
It is easier done than described.
Best Answer
The āPā trap (named after its shape, has nothing to do with urine) is there to prevent sewer gases from entering your home. It stays filled with water to form a barier.
You need it. Sewer gases are not good for you. In the right concentration they can even be explosive. Plus they smell really, really bad.
Everything that connects to the sewer needs such a barrier. Some things like toilets have the barrier built in. Sinks do not, so they need it in the pipe.
Your friend will eventually get a clog further down the pipe. This time he won't have a convenient and easy to take apart P trap for whatever crap he washes down the sink to get lodged in, so he will end up having to spend a lot more effort to remove the clog. Cleaning out the P trap (or just replacing it, if it was too gross to be worth saving a couple bucks) would have solved the clog problem just fine.