Glove, bat, balls, spikes, cup, cap, sunglasses are the basic gear you will need.
You definitely need a partner and/or instructor. A place to throw, even through the winter (since you are starting out, you should not take the winter off). You may want to set up a net, target, or backstop of some kind to throw at when you can’t find a partner. You will need to throw often.
As far as distance, just start at where is comfortable and add distance as you can manage it. Every throw needs focus and intent. Even playing catch–you are there to work. Benefit from the experience of each throw.
I would not involve a college coach, at this stage, you will not be taken seriously. The coach will probably try to find a polite way, if you are lucky, to brush you off. Perhaps if he is looking for help with equipment management or field prep and set up for practices, etc. he may take you on as a volunteer team helper which would get you exposed to college level players and you will see, first hand, what your goal really is.
As far as what you should be doing. I’d keep it simple for now. Warm up, get the blood flowing and get a bit of a sweat going before you pick up a ball. Start off slow and smooth, establish your throwing motion, then work on building speed of movement for your entire body–not just your arm. I would recommend that you start off with a coach of some kind. It doesn’t need to be a pitching coach–just someone familiar with baseball instruction.
You should throw daily until your repetitions and velocity start getting serious, then cut back to 3-4 times per week and eventually when your pitch counts get higher you can scale back to 2-3 times per week.
That should get you started.