AWS costs vs home server

The answer depends on your needs. If you are going to maintain BIG-IP appliances and VEs regularly in your own datacenter, you'll want to be testing with something similar. That way you can understand how HA failover works in your own datacenters and have access to the serial console.

You may want to use AWS if you were planning to deploy that in production. There are some differences in the networking setup and behavior that are specific to BIG-IP on AWS. Running an HA pair in AWS is also slightly different than in your own datacenter, so if you plan to do it in the future then now is a good time to get started.

You might also prefer AWS over hardware costs for very short bursts of testing or validation like API (rest/iControl) integration testing.