mp4 is the best format out of those mentioned. But it is newish & some people do not have the codecs for them. mpg generally refers to mpeg 1 or 2 which are earlier mpeg formats. AVI is not a format per se, it is a containor. The actual video & audio format within could be anything from mpeg 1,2 (perhaps even mpg3 for audio) or 4, divx, etc.
This will give you some tips:
Movie download issues (click on blue link) _ (2nd last post has information on best video formats.)
For playback problems, it is usually a lack of having the correct CODEC to play the particular video or audio within the video. Either updating your codec pac or removing the one you have & getting a decent pack. Should not have more than one codec pack as it can cause clashes & problems.
We usually recommend getting
VLC player as it has codecs builts inside & is generally very reliable. Get it even if just as a back up player.
CODECs list for Movies/Audio/ Alternate players
To change default video player, see
Setting Default video app. Basically the process is ... right-click each type of video file & choose open with such n such player, & tick the option to always open that type of file with that player. You will need to repeat this process for each video format such as mpg, mp4, avi, etc.