There is a huge range of MP4 players available. MP4 is a mis-used term that generally refers to any portable device which is capable of playing video.
They range in price from £20-ish to £400-ish, in screen size from 1.5 inch to 7inch and in storage from sub-1GB (not much good for video) to 80GB.
So, if you give us some more info on what you want to be able to do, perhaps we can give you some pointers.
In the meantime, for the cheaper end of the market, you can look here:
MP4 Site , and here:
MP4 Forums.
Video transfer varies by device. Some players will only play a specific format (typically AMV or Mpeg4), some have a video input and will encode video for you. For those that require a specific format, there is a wide range of software available on-line that will help you transfer stuff over.
Some of our fellow forum-ites will tell you that only iPods are worth considering. This is a highly subjective viewpoint.