Older models are where the specialty tools come in handy. A lot of fords required special tools to move the adjustable control arms for caster camber. Some front drive require torx bits to shim rear spindles to install shims. On the fords there were special tools for mustang II's, crown vic's, etc to set camber/caster. When you get into replacing parts worn before alignments you will need some pickle forks and ball joint press sets etc. But start off with what has been mentioned above. Whenl you run into the cars that need specialty tools, then check Ebay and here for sources of specialty tools not being used by retired mechanics. Truck and heavy duty take an entire different range of tools to set them, like I said it depends on what you run into.
One of the most important is a brain. Look at the tires coming off for tire wear and problems, recognize the patterns for toe and camber wear and adjust the cars to eliminate the wear not just to be within spec's. Also doing this you can also recognize when the alignment heads have been dropped and all the cars are the same amount off on the same wheel without tire wear to back it up.