Personally, I had to move during Covid19.  These are my suggestions:

Moving companies are deemed essential and therefore still operate.  Do your homework by getting quotes and asking what their systems are to minimize contact.  My movers wore masks and gloves, stayed 6 feet away and only handled payment through debit or credit card.  The quote was given through email once I filled out the necessary paperwork advising them of what they were moving.  They also had me sign a document that stated I had not been out of the country during the last 14 days, I exhibited no symptoms of the virus and I was not in contact with anyone who had the virus. Oh, book well in advance of your move.

I did all the packing myself and purchased the boxes through a company that again was deemed an essential service. I also moved the boxes and any small items that could fit in my car.

When it came to unpacking in the new home, the condo I moved into had their own set of rules as well. Contact was minimized.

If you or any family members are experiencing symptoms, postpone your moving plans if you can.