This circuit will be larger than any you have built. So, do carefully follow the guidelines below.
Neat assembly is absolutely essential.
Three weeks are available to you. Make use of this time. You'll not be able to assemble it on the last day in the lab.
Use bypass capacitors on your supply lines. Use 10µF and 100nF in parallel. Use the rails on either side of the breadboard for power supplies and place bypass capacitors on these.
Do some floorplanning of the breadboard before you start wiring up components.
It is possible to divide the work so that different team members start wiring up different parts of the circuit. Obviously this will have to be on different breadboards. So divide up the blocks logically so that you don't have too many connections between the breadboards.
Do not use series/parallel combinations of large numbers of components to realize a particular value. Limit yourself to at most two. If you can't find the desired value, design it with the closest available values and figure out if there is a way to change some other paramter in the circuit to meet the desired specifications.
Do not assemble the entire circuit and try to test it. Build and test each block, then connect them together one by one, and verify that it works after each step. For example, with the spectrum analyzer, you can start working backwards from the envelope detector, of forwards from the front end low pass filter.