Hey there! As a fellow engineer who's been in your shoes, I totally get the challenge of sizing a servo motor when you don't have all the mechanical data. It's like trying to pick the right shoes for someone without knowing their shoe size! Here's a practical approach that's worked for me:

First, don't panic about the 'poorly documented' part - this happens more often than you'd think. Start by making educated estimates. If you can't measure the load inertia directly, try to estimate it based on the physical dimensions and materials. For example, if you're moving a metal plate, calculate its mass from dimensions and material density, then use standard inertia formulas for basic shapes.

For high precision and rapid acceleration, you'll need to focus on three key things: torque, inertia ratio, and speed. The acceleration torque is critical - it's what gets your load moving quickly. A good rule of thumb is to aim for a load inertia that's no more than 5 times the motor's inertia for stable control.

Since your documentation is limited, build in a safety margin. I'd recommend adding 20-30% to your torque calculations. Also, consider using a gear reducer - it can help match the motor to the load better and gives you more flexibility if your estimates are off.

Most servo manufacturers have sizing software that can help. You input your best estimates, and it suggests suitable motors. Don't be afraid to reach out to their technical support - they see these situations all the time and can offer valuable guidance.

Remember, it's better to slightly oversize than undersize, especially for your first project. You can always tune down an oversized motor, but an undersized one will struggle with precision and acceleration. Good luck - you've got this!