Observation in ER vs Ambulance
If I had to pick one over the other, I would pick the ER. The unfortunate thing about doing your observation on an ambulance is that even if it's busy, you will still probably see less patients than what you would have in the ER. Because you'll probably see more patients in the ER, you'll probably see a better variety of complaints too. Another unfortunate thing on the ambulance is that there are only two people and both of them are either an EMT or paramedic. In the ER, there will probably be more than two people and multiple different disciplines: could be an EMT/paramedic or CNA working as an ER/floor technician (who may have prior experience on an ambulance), phlebotomist, x-ray technicians, LVN/LPN, registered nurse, PA, and physicians. If you don't get along with the EMT/paramedic on the ambulance or they aren't in the teaching kinda mood then tough luck. Since there are more people working in the ER, the odds are higher that you will find somebody that you will connect with or who will be in a teaching kinda mood. In my area, paramedics don't do a lot for most patients other than transport, get vital signs, and establish an IV. When we respond to calls on an ambulance, I feel like most of what we see either happened prior to us arriving (syncope, seizure, etc.) or it is a continuous problem (chest pain, shortness of breath, stroke-like symptoms, etc.). Some of these problems the paramedic might be able to treat and it will look totally different to the ER (eg I have had shortness of breath patients that are speaking 1-2 word sentences when I arrive on scene, treat them with albuterol and oxygen, and they'll practically be doing kart wheels into the ER), but in my limited experience, they'll have a problem that I'll attempt to treat, but it the change is minimal, if any (eg I frequently get chest pain and shortness of breath patients who don't change even after treatment). What I am trying to paint to you is that most of the time the problem is subjective and changes minimally, if at all, and the paramedic info that he reports to the ER is just relaying what the patient or witnesses has told him so therefore you probably won't miss a lot if you are doing your observation in the ER.
The great thing about doing your observation on an ambulance is first making yourself a familiar face to the company if you plan on applying there. If you connect well with the EMT/paramedic you are observing then they might be able to help you get in. You'll probably get to learn some operational stuff such as their posting locations, terminology they use, and observe their interaction with the fire department. When you are new, lights and sirens might make you feel pumped. It's fun. In between calls, it is mostly relaxing if you aren't the one driving to different posts. Like I said earlier, there are some calls where we do get to see the patient not looking too hot and by the time they get to the ER, the patient is practically doing kart wheels into their room while the ER staff asks us "Why did you bring them to the ER???" but I consider those calls somewhat uncommon (not rare).
I 100% agree that you should do both. I don't think people should do it just once or twice on the ambulance and/or in the ER. It's too few to really be that useful.
Stethoscope
At your level, you might be using your stethoscope for lung sounds and blood pressures. I feel like fancier stethoscopes (like Littmann) are more targeted for listening to heart tones, which most people don't even do. We had a discussion on it
here. In regard to listening to lung sounds and korotkoff sounds (blood pressure) using a fancy stethoscope vs a cheap one, it sounds the same to me. Maybe other people have better hearing than me? I wouldn't pay the extra $100 for a minimal difference that is hardly noticeable. I've tried listening to heart tones. Knowledge wise, I can describe the sounds, document it, and associate it with a condition, but listening wise in real life... Maybe other people have better hearing than me? I haven't heard too many murmurs. Even when I did hear a murmur, it was difficult for me to describe unfortunately. I think it is a pretty difficult skill.
CPR Card
Talk with the place where you did your CPR training at. Ask them about how are you gonna receive it. Like STXMedic said, they usually just give it to me immediately after I finish the class. We online folks don't know how your educational institution works so it is probably best to go to them and not us in regard to this issue.