Why is it always advisable to start a pump against a closed valve?

I'm not mechanical but I believe you are talking about reciprocal pumps with full voltage starters. This is typical for these pumps because for short periods they can operate without any discharge. Other types of pumps would either stall out or cause damage.

Reciprocal pumps also need to be primed if they start at negative pressure. To reduce the negative pressure, sometimes the valve upstream is closed until the pump is primed.

Also, depending on the type and length of pipe, water hammer is removed by starting the pump with a closed valve and opening it slowly. In this case, a soft start can remove need to close the valve before starting.

How do you size tanks for booster pumps

As I understand , Booster pumps are normally installed in an existing pipeline to boost/increase capacity of the pipeline.I'm not sure what "tanks" you are referring to.Are these storage tanks where the booster pumps are pumping to or something else?

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Why is it always advisable to start a pump against a closed valve?
With the valve open, a lot of mass will move at start up, will cause the pump, piping to shift, and connections may( will) break

Closed valve start-up is relate to motor rating of centrifugal pump.

Pump shaft power is a function of head (H) and flow (Q). Open valve start-up will result large flow passing through centrifugal pump (as backpressure is yet to developed) and causing pump motor trip.

Open valve start-up may required larger motor... :)