It is a common question for a hobbyist to ask a list of tools and components to set up an electronics lab. As most of the peoples have a limited budget, set the initial focus on the civil, architectural and electrical part. The selected room must be spacious (of around 150 to 200 square feet), preferably have 12 feet ceiling height. There should be plenty of natural light. Like any lab, there must be an adequate water supply. The electricity mains connection must have at least one miniature circuit breaker and proper earthing. There should be enough wooden racks, workbench, artificial light, security etc.
You will need a package of basic electronic components such as resistors, capacitors, potentiometer, the commonly used ICs to get started. You need a breadboards, breadboard jumper wires, at least a multimeter.
The next thing you’ll need is a DC power supply. It can be as basic as a few dollar worth power supply, or a DIY Benchtop Power Supply. I believe that a good bench DC power supply is costly to many hobbyists. High-quality bench supplies have a long service life. Their number of units sold per year is so less that it results in much higher manufacturing costs. Do not jump to purchase one till you know what are advantages they offer, what protection they need.
An oscilloscope is a next instrument. USB logic analyzers are cheaper tools for digital signals, definitely better than having no tool at all. But, probably mostly those who will do some advanced work will need both an oscilloscope and a logic analyzer. Only budget-saving tips about oscilloscope are to find a used oscilloscope that can be serviced by the manufacturer.
Coming about the function generators. You’ll not need a function generator for present common works done by the hobbyists, however, there are cheaper DIY solutions that can be used to have something, rather than nothing.
Do not forget to have a video camera to record what you are doing.