This is a standard drawing for a basement plumbing drain layout.                                                About Venting

In some areas you may need a backwater valve.                                                                              New Work Venting

It depends on the engineering in your area.

It is still good practice to use one any way.

All drains must be installed to provide a minimum slope.

Away from the fixtures of at least 1/4 in fall per foot of pipe length

And you have to have a really firm packed base.

You need to remember that except for toilets or "water closets" which is the proper terminology.

The total fall from the fixtures trap cannot exceed the diameter of the fixtures drain.

Also keep in mind that the maximum distance you can put between a vent pipe and a fixture trap will rely on pipe size

In some cases you may be required to use expansion joints to allow for expansion and contraction