Could I use 25 Arduino Pro Minis with along with 433 MHz RF receivers?
Yes, that is easy if you don't intend to address more than one servo at any one time. Each Arduino/receiver would have a unique address and would respond to a command message addressed to it only. The controlling computer would need only one transmitter. To address more than one Arduino, a single message could contain more than one address+command. You will need an error-detecting transmission protocol and the VirtualWire library would work well for this.
What would the best way to then have each arduino communicate with a computer?
In principle, the same idea would work. However, in practice this is much harder, because only one Arduino can be transmitting at a time to the central computer. The problem is how to synchronize the different Arduinos so their transmissions don't overlap.
Home weather stations with remote sensors solve this problem by having the sensors transmit short messages very rarely, every once every 30 seconds to 2 minutes (or so), so that the chances of two sensor transmissions overlapping is small. In that case, it is not a great loss if a sensor reading is missed.
If the occasional loss of a return message would be serious for you, then you need a much more complicated messaging protocol, such as those implemented on Xbee radios, etc.
Another approach would be for each Arduino to use a tunable transceiver with at least 25 available, non-overlapping channels. Pololu offers the inexpensive Wixel, which in practice has about 128 well separated channels.