Ipods seem to be the most popular in that price range. Not all ipods play mp4 video. I think its primarily older models and or newer but smaller models that don’t. You can find out which do as well as a lot more information in the wiki.
I’m pretty sure they are still making different generations and different models of ipods as I see them advertised. You can of course see what the current models are on apples site.
If they are not still making some, you might just have to do a little shopping around to see which are still available new. Unfortunately, mine are all cheaper than ipods so I cannot give you any personal experiences. I have looked at getting one a few times though. There are only 2 problems that I have found with them. If you plan on buying protected music online from a service, you can buy from apple itunes only! Music from other music services wont work. You can of course play any unprotected music like stuff you convert yourself. Apple also likes changing the firmware on ipods to intentionally make it incompatible with other companies accessories. If you want to use it with a dock or a larger video screen or similar accessories, they may not work if you got the wrong model and or wrong firmware unless they are apple accessories. Beyond that they look pretty good.