A) You'd want to go with SATA drives over PATA (IDE).
Best bang for buck for the storage part would be a pre-made NAS, as doing that through/with a Pi is NOT effective (i'm going to replace my self built drive rack with a proper NAS along the line), or worth the time, unless you magically have all the needed parts, cables and whatnot (i did cause i'm a packrat), but it'd still be very time consuming.
I agree with Keith on this : the Pi CAN do it, but it's not the right platform for it.
His suggestions for turning an old PC into a NAS are also excellent alternatives for buying some expensive premade NAS unit.
B) Power supply would be included with the NAS, so not an issue, for Pi power see E.
C) Pi could be used for the Media server/center bit, using it as the media player or as the main interface to the NAS, on top of the NAS just doing it's thing on the network as a share.
D1) Software takes a bit of learning, but for a mediacenter/server/player OpenElec and RaspBMC cannot be beat.
Both are VERY userfriendly and most things will work right out of the box, at the worst we'd have to teach you how to use the command line to update stuff or add files/dependencies, although both RaspBMC and OpenElec take care of the updating on their own, without much user interaction.
I'd suggesting looking at running
NOOBS (don't be put off by the name), which lets you install several OS'es on one SD card.
D2) Software cost is none, because GPL/Gnu/FosS/Linux.
D3) Custom code can be needed, but the Raspberry Pi forums are full of very friendly and helpfull folks who are often more than willing to help.
E) Pi's can be bought just about everywhere, even Amazon. Adafruit is an obvious choice for parts as well.
You'd typically want a Pi, a 4-8 GB SD card (class 10!!, and i suggest getting at least 8Gb's), a small enclosure (Adafruint, Cyntec, PiBow, Stackable, PiFace) and either a powered USB hub like the PiHub i showed in the 'random buys' thread that will also power the Pi, or just a small telephone charger (1-2A, 5v) and a self-powered USB hub.
The phone chargers are usually sold by the shops that carry the Pi's, but i want to stress that something like the PiHub is the best solution for clean power and connnectivity.
If you go the WiFi route you need to look into which USB dongles will work with your Pi OS of choice, but that isn't too hard to find out.
Other than that i have local sources, so i can't be of much help there.
Cost is what you make of it, a Pi with PiHub and a simple enclosure shouldn't be more than $60-$70 (many stores will sell complete kits for about tht, which will include the SD card, usually pre-imaged and ready to go), Wifi Dongle will be from $5 up to $20, depending on brand and type, NAS would be the most expensive part really.
Although a NAS isn't always necessary : a simple SAMBA share on your Windows PC could suffice, you download/attain by legal means the media you wish to play via the RPi, add to share, make sure Pi is on the same network, type info for the SAMBA share into the RPi's OS, and Bob's yer uncle.
For example, my dad's music collection was turned into MP3's, put on a SAMBA share on their living room PC, and the RPi in the kitchen can stream all that content.
A NAS would work the same; setup NAS, connect to your LAN in whatever way you plan to, note down IP, point RPi to it, presto.
Assuming you have a modern TV with HDMI, the Pi hooks up to that, and any sort of luxury speaker sets you may have hooked to the TV will keep working as before.
If you want to control the Mediacenter with whatever remote(s) you may have lying around, you can invest in a Flirc dongle (around $20), and then you have luxury at your fingertips.