Quick Blu Ray question

If your TV passes deinterlacing tests it will set itself to 1080i.
If it doesn't, it will run at 720p.

Just set it to auto and let it do its thing. The difference will be so minor that it will be very tough to tell. 720p and 1080i are different types of interlacing and the difference between the two is very small.

I hope this helped.

It's depend mainly from the TV.

There are mainly 4 HD resolutions:
-720p is 1280x720 progressive (ie, every frame is made by 1280x720 pixel and the framerate is 50 or 60 Hz, depending where are you from - US is 60, Europe is 50)
-720i is 1280x720 interlaced (ie, every frame contains only half of the resolution, one frame with the odd rows, the other with the even rows).
-1080p is 1920x1080 progressive (it's availvable only from Blu Ray players, not from broadcast)
-1080i is 1920x1080 interlaced.

If your GF tv has FullHD resolution (1920x1080 or more) probably 1080i is the best choice (between 1080i and 720p), but if the resolution is 'HD Ready' (1280x720 - usually 1366x768) probably 720p is better.
1080i has an higher resolution than 720p, but the quantity of 'data' inside the flow is very similar and if your tv is 1280x720 native, it has to reduce the resolution by interpolation if you sent to it 1080i.