markjhaner,
Welcome to the Shopsmith Forum.
As for your questions the answers will vary depending on personal opinion and needs. Your questions are in the quotes below with my answers.
What are the basic must-have tools for a beginner woodworker?
This depends on the type of woodworking you wish to do. Some like hand tools to complete their projects while others prefer power tools either handheld and/or bench tools. Tools for cutting, shaping and assembling projects are needed items.
What tools or functions can the Shopsmith replace in a compact shop?
The most common Shopsmith Tool is the Mark V which has different models in which the Table/Fence System varies. The Mark V is a 5 in 1 tool able to be a Table Saw, Disk Sander, Horizontal Boring Machine, Drill Press and a Lathe. These are functions that a Mark V can replace individual tools. The Mark 7 add under and over table Routing and Shaping. You can add SPT's (Single Purpose Tools) to the Mark V or 7 to increase the functions. There is a Jointer, Belt Sander, Bandsaw and Strip Sander that are currently in production. On the used market you can find the discontinued SPT's like the Jig Saw, Scroll Saw, Planer and from time to time one of the Air Compressors all made to attach to the Mark tools to power them.
Any tips on how to save space while still working efficiently?
The Shopsmith Mark tools can have Retractable Casters made for them attached to the legs. This allows the Main tool (the Mark V or 7) to easily be moved around the shop and stored out of the way when not in use. The SPT's mentioned earlier can also be stored out of the way on shelves, carts or other methods. I have my primary SPT's (Jointer, Jig Saw, Belt Sander, Bandsaw and Strip Sander) on a cart with many accessories. I keep my Scroll Saw mounted on a Power Station.
If you would like to know more about the Shopsmith Mark V, its history and evolution check out the topic
Shopsmith Mark 5 What When and Where in the
Community section at the link below.
viewtopic.php?t=24963
There is also a topic called
SPT's What When and Where you may find helpful.
viewtopic.php?t=26072
And if you want to know about the Shopsmith tool that predates the Mark V see the Topic
Shopsmith Model 10's What When and Where at the link below.
viewtopic.php?t=23647