The Samsung P3 has top notch format support, a great capacitive touchscreen, Bluetooth 2.0, FM Radio, and even supports Flash. It's a bit more than you wanted to spend but it's among the best mp3 players on the market.
I own a P3, and there is no mini SD slot. That's really the only shortcoming. I used it on my previous player, but now it resides on my smartphone.
It's a samsung, so it follows that the screen is awesome. Much better than competitors. It beats an iPod touch's screen senseless. It is however behind in not supporting multitouch, but it is capacitive. Which means items in your pocket wont activate the screen.
It has flash support, which is nice for asinine games to waste time. I don't use it that often as I bought it as an MP3 player first and a media device second. The touch screen works well with flash games, no complaints there. I am a guitarist so I have to use my right hand as the fingers on my left hand have callouses and make it difficult for the screen to detet.
Audio quality is top notch. I had a Sansa Fuze which is widely regarded as one of the best sounding MP3 players, and through my Sennheiser headphones the Samsung sounds just as good to me.
File support is great as well, OGG, FLAC, MP3, WMA, AAC, MP4 all work. Tag recognition on some is a bit spotty, but luckily there is a file browsing mode so i can access the music that doesn't have tag support. I keep my music strictly organized so it works out pretty well. At any rate I recommend using a 3rd party app to get your Tags under control. It simplifies matters greatly.
Video support is on par with larger and pricier systems. I was able to drop an .avi movie and an .mkv in and without converting the P3 was able to resize the image perfectly and get a proper aspect ratio. I was able to watch 2 movies back to back on a flight to hawaii on it without running down the battery or tiring my eyes. In fact the battery lasted the rest of the flight and 2 more days in Honolulu before I had to recharge.
It does have it's own apps, but to be honest I haven't looked into them that much. Sense it has flash support anything I need I find a flash program for.
Copying music is easy. the is MSC and MTP modes that you can use. This means PC, Mac and Linux are all supported for drag and drop file access. I prefer it this way and load it up like a usb drive. You can also use their program emodio if you want, but i don't bother. IMO this is a major strength that almost every MP3 player has over Apple products. With an iPod you have to format it for mac or Pc, not both and you have to use iTunes. I have hooked my P3 up to all three major platforms and used their audio programs of choice without incident.
Forgot build quality.
The case is metal. Either aluminum or magnesium. It's solid and shows no signs of giving way under pressure. After owning it for 6 months I have little to no scratches or abrasions on the screen or case. It looks practically new. It is a very solidly built device.
I know what you mean by the screen. I have a Samsung monitor myself. I love it.
I have a Sansa Fuze myself. It is refurbished, but it hasn't failed me since I got it 1 year ago. Sound quality is good.
I keep my music organized as well. A few months ago, I edited ALL my music using Winamp, editing songs that didn't have albums, that didn't have the song titles, but the file had a name. Took me nearly all day to do it, but it was rewarding. I have 12GB of music, but I can easily swap in and out albums.
Battery life is a good thing. I never watched movies on my Sansa, but it took a long time to convert them.
I use my Sansa through USB on my Win 7 PC. iTunes is dead in my ****ing head. I hate it. Yes, on Macs it is fine, but for PCs, it fails.
Build quality is important. My Sansa took some beating, but it has survived. I love metal, not the music. It would show it's worth, I would think. I do hate plastic....
Yeah sansa's are solid, the titanium case helps a lot. ironically my was killed not by a physical failure, but by firmware corruption. Their screens aren't much for video, but for a straight forward music player I recommend them.
Last time i checked the P3 comes in different capacities. Mine is 8GB. For comparison sake, I have a samsung blackjack II smart phone and the P3 is just as tall, but thinner and narrower than the phone.