My son developed one for his final year project. It worked well - front-end design is critical though, he dead bug prototyped that section before committing to PCB. As others have said, it is essential that it is battery powered (including not being capable of use or connection to the body leads if USB charging!). This is a safety red line, as well as a potential signal integrity nightmare in a home project.
As far as other functionality, think of a hospital. An ECG test tends to be a standalone activity, while standard 'Obs' combine blood pressure, temperature, and pulse oximeter. Even in theaters and HDUs, the ECG is a standalone machine.
It's important that if you are doing this, it should be undertaken as a personal interest project rather than with a view to a commercial product - approvals will kill you.