Hi Rohan,
Here are my thoughts,
The mac mini is a very robust desktop and OSx is a very strong platform to setup for media server/file server duties. What is your skill level with computers? Are you an advanced user?
1. Mac Mini 2.5 GHz dual core i5 processor with 500GB HDD and 4GB RAM (Could also go in for the quad core i7 1TB version but its $200 more)
If you end up purchasing the late 2012 or 2013 mac mini then you can upgrade the HDD. It has the space for an extra drive as well. So effectively you can run it with 2 internal HDD. The minis use Laptop HDD, if you buy the disks here in India then 1TBs are your best best effectively giving you 2TB of internal space. If you buy the disks from the US, then you will get 2x1.5TB = 3 TB of space. Either way you will void the warranty on the mini. My 2012 mini runs with a 500GB and 1 TB.
But why a mac mini? for the price you can get a better speced desktop with better expansion capabilities. (eSATA)
2. Plex Media Server loaded on the mini and plex mobile apps on the iPhone, iPod, iPad.
Do you actually consume your media in so many devices, it is pretty difficult to watch a movie on your iPhone/iPod. Which brings me to the question why Plex? If you are consuming over apple devices only as per your list, just iTunes Home Share is enough.
3. 2-4TB drive connected to the Mac Mini on USB 3.0
First 4TB external are at the moment power assisted only and are priced > 12K INR. 4TB Desktop Internal HDD have not stabilized in the market and it would be best to avoid these for sometime. I do have a Seagate 4TB external, which is doing very well, but it is still a risk.
Second, If you have large BRRips on your ext HDDs you may see performance problems. If you do go with the Mac Mini, then going in for one of the thunderbolt based expansion boxes will give you better performance and expansion ability rather than USB 3.0.
If you choose to go with a normal PC, then an eSata card and an JBOD box will definitely be the good way to expand.
I am running a ubuntu server with 5 * 3 TB Raid 5 Array of which 4 Disks are on board and 1 Disk is in a SansDigital JBOD box. Originally the plan was to set it up as a (n-1)*3TB - 12 TB Volume, instead made it a 9 TB volume with 1 Disk as an auto spare. When one disk fails in the array it will auto replace it with the spare drive and will notify me via email
4. Setup one partition of the HDD as a Time machine backup
Which HDD are you going to partition for Time Machine? You are ok as long as this is on one of the externals. You will have to worry about space though, if you want to back up everything including whats on the external drives as well in time machine. If you are backing up only your system then how are you protecting your music and movies?
5. Use SecuritySpy software which pairs up with the mac to work as a surveillance system for the home.
No comments here, there are many options and I am sure this one is good as well. You will have a lot of video files generated and the quality of the video will decide how much space you will require to store them, you might want to plan this as well.
B Rgds,
Raj.