$1000 - for test gear (2x meters, cheap scope, USB LA, maybe a cheap LCR)
$400 - Hand/power tools (sidecutters, screw drivers, cheap cordless drill etc)
$500 - for general work room stuff, (desk, chair, workbench, lots of multicompartment storage boxes)
$400 - of generic parts stock, resistor kits, caps, jellybean semiconductors etc..
$800 - desktop or laptop computer
$900 - generic software licences, (win10/msoffice, cheap pcb design package, misc other minor licences)
So i think $4k is probably more reasonable to go from an empty room to a usable electronics lab.
Could save a little if you went all open source software. But still be looking at ~3k.
There would still items/gear missing, but that would setup a lab that's usable.