LTSpice is a free, but very capable and popular device / circuit simulation package (it also performs circuit capture and has a waveform viewer). It will be difficult to beat this one, but playing with it may give you some ideas.
One thing that comes to mind ... DSP is an area where mathematics, electrical engineering, and software come together. It is beautiful, it can be tough, but it is very useful to know and apply very widely.
When you do DSP work, you often work with sample datasets, trying to improve or improve algorithms / filters / electronics, etc ... I used a fairly simple but useful program called ScopeDSP for this, and I often thought about that I’m folding myself, but I never had time. There is another program from the same company, ScopeFIR , which is used to design and analyze the final impulse response (FIR) of digital filters. Programs are not too complicated (not intended for puns), and with a little knowledge of DSP, you can try something in this direction.
The PCB platform is a completely different payroll, and other types of EDA software (such as IC design) can fasten your hair very quickly. I would avoid these, although I know a couple of smart guys who always work on their PCB autographs ... of course, it's a difficult task, and answering machines are one of those problems that do not have a single solution. There are all kinds of compromises with answering machines, and you can usually play them apart. Having found out that the user should be able to adjust / restrain by what amount and when the route is “good enough”, it is not black and white.
In any case, maybe something there will give you something to chew on for a while. Good luck.