Daytime beer definately..:)
2) your personal sewer line (between your house and the street) is partially/completely blocked (tree roots or collapsing).. Same thing will happen if you have a clog somewhere as it goes out of the house.
It's 90% likely this is it.
Drain systems are actually really simple. It all works with gravity. Basement showers are the first place to show a main line sewer backup because they are usually the lowest opening to the plumbing system.
If the line to the street is blocked then the water that goes down the drains in your house (sinks, showers, and yes, toilets) will fill up the drain pipes in the house until it finds a way out. Bingo! Your basement shower is the lowest hole in the drain system.
There's really only one way to fix this: snake the drain. Hopefully you have a sewer cleanout somewhere in the basement. That will make this easier. If not, you can also pull up a basement toilet. This is something you can DIY, Home Depot rents snakes. It's nasty though. A pro will probably charge you in the neighborhood of $200-$300 to do the job. On the higher end if they have to pull up a toilet.
The way forward depends on what comes back stuck to the end of the snake. If it's toilet paper and sludge... that's good news. Switch to a cheaper, septic safe TP (means it breaks down easily) and you'll probably not have this problem again.
If the snake comes back ensnared with roots, dirt, and bits of clay pipe... then you have a larger job on your hands. I don't have much experience here, but I know that putting a lining into old sewer pipes is becoming increasingly popular. Might be worth doing some research into that before digging up and replacing the line.
Have a beer. If you are going to DIY this, have a couple.