What is the best way to size chilled water pipes? is it correct to use velocity method for small sizes but the pressure drop for bigger ones?

This is the common practice check ASHRAE HVAC Fundamentals [2013] F22 SI page 22.5 :

A variety of upper limits of water velocity and/or pressure drop in piping and piping systems is used. One recommendation places a velocity limit of 1.2 m/s for 50 mm pipe and smaller, and a pressure drop limit of 400 Pa/m for piping over 50 mm. Other guidelines are based on the type of service (Table 8) or the annual operating hours (Table 9). These limitations are imposed either to control the levels of pipe and valve noise, erosion, and water hammer pressure or for economic reasons. Carrier (1960) recommends that the velocity not exceed 4.6 m/s in any case.

here is the online link which helps you a lot.

https://www.tlv.com/global/TI/calculator/water-pipe-sizing-velocity.html

In McQuay pipe sizer:-

4f/s maximum for pipe below/equal to 50mm and 4ft/100ft for pipe greater than 65mm pipe.

• Sizing pipes have to flow to the extent necessary and appropriate speed.
• The size of the pipe must be such that high speed water flow creates noise and reduce the life of pipesNshvd.kahsh corrosion due to water flow rate in the pipes should be made to the extent that unjustified increase in the cost of plumbing pipe diameter does not increase.
•     In order to reduce the effect of water hammer in the pipeline, should be controlled flow rate.

the best way to size chilled water pipes is of small diameter. and the it should be make up of copper (cu) because it can't get corried and remain cool for a long time and pressure doesn't drop here.