Should I rather be shooting 1080/50i or 720/50p for 25fps web use? The camera here is a Samsung HMX-Q10P (P likely stands for PAL: the N model would have 60fps instead).

The videos I upload usually are 25fps either way, but strictly speaking 1080/50i will never give me the odd lines when dropping every second frame, so I rely on the deinterlacing algorithm of my video editor (Shotcut in this case which may use ffmpeg or other stuff internally) to deliver reasonable content.

I've made a few attempts at fast moves of the camera shooting 1080/50i and I have not been able to see noticeable staircasing when creating 25fps output from that by reexporting from the video editor.  However, I am not sure how much quality deterioration the interpolation of the odd scanlines will cause.

So assuming the desire for best results, would I be better off shooting in 1080/50i or in 720/50p for videos without global movement (fixed mount, no zoom while shooting) and moderate local movement (close-captured single musician), and how would those considerations change given different material?
If you're mainly concerned about the staircasing, consider where the video will be watched. If interlaced video is shown on a display made for interlaced video, it appears ok. If you play it on a progressive display (such as a computer monitor) the staircasing is easily noticeable even for little horizontal movements (of the camera or of the subjects). For details see https://cardinalpeak.com/blog/interlaced-video-and-computer-monitors/

Best is if you never have to deal with interlaced video if possible.