A lot of simulations. There is essentially nothing that only has advantages or disadvantages, so you need to consider tons of options.

If you have a given rocket design and a fixed mission: Launch at full power - this is a very wasteful part of the flight and you want to gain speed as soon as possible. Acceleration will (almost) always be low because the rocket is still full of propellant. Tilt a bit to the side and follow an approximate gravity turn. Throttle down before reaching the maximum aerodynamic pressure if needed for safety. Typically this is only a pretty short period.

Some more things to consider, in addition to what you mentioned:

• Different payloads have different requirements but you don't want too many rocket variants.
• Making the rocket more robust against weather helps with launch opportunities but might reduce the performance.
• Typically components are shipped from construction site to launch site, favoring a smaller diameter - but that makes it more susceptible to wind.
• Launch site selection matters, too.