How exactly do commercial pick-and-place machines generate and manipulate vacuums?
The pro machines have dedicated vacuumpumps from companies as Busch and Edwards which costs 4 to 5 figures.
Sometimes you can pick them up cheap at auctions.
If you buy the low end vacuumpumps (<$100) make sure they go as low as 50kPa (500mbar) (0 being absolute vacuum and 100kPa or 1000mbar being normal environmental pressure)
which is IMO what you at least need for handling heavier packages.
For only resistors , caps etc you can get away with less vacuum.
If you have a cheap pump it normally doesnot have a high flow rate, meaning it takes forever till your vacuum level is reached.
You can use a small iron pressure vessel (old scuba tank that is out of date can be get for $20 for instance) that you use as a buffer.
It kinda acts like a capacitor for voltage

Then you can run the pump for an hour before working and have a nice buffer.