Ok i'll try to sum it up from all the research i've done for your case cenario:
XBMC does hardware and software decoding on PC's and supported devices (often not officialy supported). Won't do transcoding thru UPnP built-in server in case you want to stream your XBMC video library in other devices, so only file types that are natively supported by those devices will play.
PLEX and Media Browser will Direct play or transcode. If the file type is fully compatible it will Direct Play, if part of the file type is not compatible then transcoding will be needed. Using this kind of services will let you stream your media to a wider type of devices often already own and often not so powerful, plus you'll be able to stream your media outside your LAN network - anywhere, anytime while you have an internet connection.
A NAS is excellent at basic NAS tasks, but most can't play high bitrate, subtitled MKV's without transcoding. No cheap NAS will be able to handle transcoding HD movies, they are just not made for it.
I PERSONALLY USE XBMC AND PLEX and now looking at Media Browser. Many in here do the same, though Media browser seems to be more popular lately.
That being said there are a couple of solutions depending on your budget and other factors...
SOLUTION #1
The simplest solution is a cheap NAS/DAS + a decent front end client (eg: WD TV live, Roku, HTPC) that can do alot more than just play movies. Depending on your video collection, you may need something with some more cpu/gpu power, enough to play high bitrate videos (eg: Hi10P, 20mbps) and Live TV codecs.
So the NAS/DAS would do points 2 and 3 of your list no problem while the HTPC with decent specs will do points 1, 4 and 5 nicely.
http://youtu.be/PaNIksfm8kw?list=PL-x30K...gII9vkt7Ac
THINGS TO NOTE:
- A DAS (Direct Attached Storage) setup can be faster and more reliable IMO. You can pick the OS that will handle the shares, etc and use BitTorrent Sync for unlimited file-syncing on a PC, Laptop; but it will obviously lack the advantages (in certain NAS) and purpose of a NAS.
- Remember that the client devices (eg: tablets, game consoles, android boxes, media player boxes like roku, boards, NUC,etc) will have to do all the work so pick wisely.
Make sure they can run XBMC stable enough and that can play all your high bitrate/live TV/in general media no problem.
In case of Plex/MB, devices must be compatible with the type of files you want to play:
* Fille Container
* Video Codec
* Audio codec
* Subtitlle format
... otherwise transcoding will be needed.
- Depending on how much storage you would like to have to start with and if you care about data integrity (will cost you more), you can start with a cheap 2 bay NAS for under $200 or if you want something more future proof then you could get a 4+ bay NAS like the Synology DS1513+ with 5 bays or the DS1813+ with 8 bays or the Qnap ts-470 with 4 bays, 2gb ram, core i3. All DISKLESS with really good reviews BUT over $700. For that amount of $ you could build a high end media server and do some good gaming.
- If there is a drive fail, restoring data could take even days in a cheap NAS and their slow CPUs. and you will pray there is no other drive faiure while restoring and that everything ends well
- If i had to pick a NAS i would go with Synology and it's latest DSM no doubt because is stable, best feature rich, great support, great community behind.
SOLUTION #2 (DIY - Do It Yourself)
A home built NAS/HTPC will be much better at handling all you need including transcoding, but you'll lose the extreme ease of use that comes with a NAS and will need to put in more effort to build it, set it up as you want and maintain it.
So this solution will do all the points in your list and much more right there in a single custom build.
Oh and if you need the "Dropbox like" feature then you can use BitTorrent Sync for unlimited file-syncing.
THINS TO NOTE:
- It is not recommended to have the storage and the media player to play all your media (eg: XBMC) in the same place, so many would advice you to get a dedicated client. Something like a NUC or Chromebox so you can still play your Steam games. This is optional and all up to you.
- a Quad core i5/i7 processor (High CPU mark), 8 gb RAM, SSD for the OS, a MoBo with at list 4 SATA III 6 gbps ports, Gigabit ethernet, USB 3.0 ports are min specs i would pick - future proof. A Mini-ITX build will look better in a livingroom but may not be ideal for the amount of Hard Drives that will be required.
https://fanart.tv/2014/01/build-nas-media-server/
- Most likely you will be able to stream your media content in devices you already own if you build a powerfull PC that can transcode to multiple devices at the same time.
So this will be handy for devices where you can't install XBMC, then using a third party app like Plex for example will have you covered.