I am thinking about putting a shower, sink and toilet in my basement laundry area. There are no roughed in plumbing lines for this. In trying to decide on the location of my toilet versus the shower and sink, I need to know the order in which these three should tie in to one another before tying in to the main drainage line. Also, how do these three need to be vented? I will have to do some digging and obviously do not want to spend more than necessary.

To do a good rough in we'll need Speedballs help and I was surprised he wasn't already here. My post puts you back at the head of the line and Tom will be herer shortly. Does your current sewer line exit through the wall or from below the floor and how far is this from the proposed site?

The sewer exits through the floor and I am proposing to put shower, sink and toilet relatively close to the main stack and over tha sewer line as it heads to the street.All three will be within 3-4 feet of the main stack and 2-3 feet at the most from the sewer line. If my stack is east and the sewer runs to the west, I want to put the sink on the immediate west side of the stack and then the shower drain within 3 feet of that,directly over the line as it runs west . The proposed toilet would then be about 2-3 feet directly North of the shower .

We have a problem already.
I want to put the sink on the immediate west side of the stack and then the shower drain within 3 feet of that,directly over the line as it runs west . The proposed toilet would then be about 2-3 feet directly North of the shower
The sink will be fine connected to the stack as long as bit's vented to the outside or revented back into a dry vent. However you may not connect the shower directly over the main without separate vent for the shower.
Most bathroom groups are roughed in like this.
Toilet connects to sewer main . Lavatory connects to toilet drain and runs a vent off the top the stubout tee out the roof or revents back into a dry vent in the attic.. The toilet wet vents through the lavatory vent and the tub/shower connects to the lavatory drain and is wet vented by it. This is a normal rough in and is acceptable both by local and state codes and also The Standard Plumbing Code Book in 90 percent of the country. Check your local codes.to make sure you're not in the excluded 10 percent.. The vent off the lavatory may be run out the roof or revented back into a dry vent in the attic or if you're reventing back into a fixtures dry vent you must make your connection at least 6 inches over that fixtures flood rim.
Let me hear your thoughts. Tomk