This is just a suggestion, certainly not the only possible approach.

Step 1: Get a handful of small linear actuators with a builtin controller. Some actuators have no controller, and will require one H-bridge and one analog input each. You do not want these. I have seen some actuators with built-in controllers that can be driven just like servos, I would suggest you get some of those. At this point you should carefully look at costs when choosing the actuators.

Step 2: Learn how to drive those actuators from an AVR-based Arduino, like an Arduino Uno, using the Servo library. I believe you can drive up to 12 actuators with a single Arduino.

Step 3: Drive them using two Arduinos in a master-slave configuration. The master would be a beefy Arduino, like a Mega or a Due. It would send commands to the slave using, say, an I2C bus. After sending the set points for the actuators, it would send a "go" order to the I2C broadcast address. The slave would be the Uno. It would interpret the commands and actually drive the actuators.

Step 4: Replace the Uno with a bare ATmega chip. An Uno is an ATmega328P at heart, but depending on the program size, you may get away with an ATmega48A, which is the same thing only with less memory, and dirty cheap. If you can make your program work with an 8 MHz clock, then use the internal oscillator, which will save you having to buy an external resonator. All this is to keep the costs reasonable.

Step 5: If everything works at this stage, it's time to scale up. The same master Arduino, and one bare ATmega for each dozen actuators.

This is just a suggestion, certainly not the only possible approach.

Step 1: Get a handful of small linear actuators with a builtin controller. Some actuators have no controller, and will require one H-bridge and one analog input each. You do not want these. I have seen some actuators with built-in controllers that can be driven just like servos, I would suggest you get some of those. At this point you should carefully look at costs when choosing the actuators.

Step 2: Learn how to drive those actuators from an AVR-based Arduino, like an Arduino Uno, using the Servo library. I believe you can drive up to 12 actuators with a single Arduino.

Step 3: Drive them using two Arduinos in a master-slave configuration. The master would be a beefy Arduino, like a Mega or a Due. It would send commands to the slave using, say, an I2C bus. After sending the set points for the actuators, it would send a "go" order to the I2C broadcast address. The slave would be the Uno. It would interpret the commands and actually drive the actuators.

Step 3b: Change the master's program to pretend it is controlling many slaves, and a total of 1000 actuators. In reality, all the slaves would have the same I2C address: that of the unique slave actually available. This will tell you whether your master is powerful enough for the job, and you will see how the performance scales.

Step 3c: Optimize the slave's code. Try to have it work with an 8 MHz clock, and use as little flash and RAM as possible.

Step 4: Replace the slave Arduino with a bare AVR chip. You will have to learn how to program it via ISP, but the information is widely available. An Uno is an ATmega328P at heart, but depending on the program size, you may get away with an ATmega48A, which is the same thing only with less memory, and dirty cheap. Or even with a still cheaper ATtiny. If you can make your program work with an 8 MHz clock, then use the internal oscillator, which will save you having to buy an external resonator. All this is to keep the costs reasonable.

Step 4b: Test, test, test. Last chance to change your mind before committing big bucks.

Step 5: If everything works at this stage, it's time to scale up. The same master Arduino, and one bare AVR for each dozen actuators, each with it's own I2C address.