A good choice for the ‘new’ sampling frequency is 250 Hz, although any frequency in the range of 250 to 1000 Hz will work. The bandwidth of a normal EKG is about 50 Hz, but any abnormalities increase the bandwidth to 100 Hz. A sampling frequency of 250 Hz or higher results in a Nyquist frequency of at least 125 Hz, so you can effectively filter your resampled EKG with a sampling frequency of 250 Hz.
I would use the Signal Processing Toolbox resample function, since it does everything you want.
[p,q] = rat(250/44100);
EKG_New = resample(EKG_Original, p, q);
Any filter design (Chebyshev, Butterworth) should work. If you want to design a notch filter, I would use a Chebyshev design, since it produces a short, efficient, filter with short transition regions. Also see Remove the 60 Hz Hum from a Signal (link) for a relevant example.