First, you'll be restricted by your local code. Otherwise I would suggest using copper for pressurized pipes, such as water supply, and PVC for drains as they don't need to be as durable.
I have just about zero experience with plumbing, with one glorious exception.
Our house is new, just one year old. Local code allows, and the builder installed, PVC-type from the main city supply pipe. He installed copper in the house. We had numerous leaks and breaks in that PVC pipe in the first year, mainly due to poor installation techniques. One design flaw in the installation had the pipe making a horizontal 90 degree turn to enter the foundation and then a vertical 90 degree turn to join the copper house piping at the shutoff valve. The water pressure kept causing seperation and breaks at those joints. Even after two refits/realigns, the PVC pipe was still seperating and breaking near the foundation. We also had leaks along the 130 feet of length of pipe from the main supply (it had numerous connections).
Primarily, the problems were installation errors by incompetent plumbers, but even different plumbers using the "good" glue couldn't keep the PVC joints together.
Finally, I had enough and had the entire supply line replaced with copper with a protective sleeve over it. Not a single problem since then.
Yes, copper is expensive, but it is more durable and probably better suited to certain applications such as the pressure lines. If you do need to fix a bad connection joint, I would guess that copper is much easier to re-solder as opposed to breaking, recutting, and regluing the PVC.
It looks like you're working with drain lines only, so the above info might not be of use to you. If that's the case, I think you'll be fine with PVC. Large diameter copper probably will cost a bundle.
For your #2 issue above: get that fixed. If that pipe ever backs-up it will leak into your basement. Not to mention that it will let odors into the same area. Is it accessable from the basement?
HTH and good luck.