options: raid on the motherboard (software raid) where all the xor calc is done by the os.
software raid card: sort of the same thing as the mobo raid but its on an add in card (obviously).
hardware assisted raid card: basically software raid but a little bit better performance
hardware raid card: contains a processor (and usually ram) on the card to do the xor calculations... this makes it much faster than any of the other options since it has its own ram and cpu dedicated to just this one operation... that also means its gonna be 300 bucks at least.
rebuilding is done via the software or raid card bios and its something Ive not had to do too often but on an HP server its pretty self explanatory just boot into the bios or use their smart start cd and find the option to rebuild the array. Some cards allow for online rebuilding which allows you to use the rest of the pc while it initializes in the background which is nice cause you dont feel like its doing anything. Others you have to wait for. Time is dependent on the size of the array and the amount of data being recovered. Can be an hour or two (without the online recovery thing) or it can be a few days. It all depends.
Adding your drives to your array is possible if your card (assuming you arent using the mobo) supports online capacity expansion (OCE). Just plug the drives into the card and have the software or bios initialize them and there should be an option to add them to the array. Ive not done this but look for a tutorial online about OCE and it will tell you how... you SHOULDNT lose your data doing this either ... as long as its not a raid0 that is.
your differing sizes issue goes like this... the smallest partition wins. So if you have a 1tb and a 2tb partition the 2tb into 2x1tb and you have 2 disks to add to the array so that could be your 3 drives for the raid right there... not a good idea no but i believe its possible to do that ... just remember all partitions or drives will be set to the size of the smallest partition in the group so plan ahead.
the biggest issue machine wise for specs to worry about is the power supply. If you dont have enough juice for all the drives to start at once then it might blow your psu. Other than that Id say any mid level pc can do the job unless you wanna use the mobo raid.
My set up went like this...
Was upgrading my game rig so I took my old dual core allendale 2160 on an asrock 4coredualsata2 motherboard (which was key for me at the time). Put this setup with 2gb of ram in another box and bought a highpoint rocketraid 2310 (hardware assisted software raid card). the card has 4 sata 3gb/sec ports (and each port is on its own channel as opposed to there being 1 or 2 channels which would be a bottleneck) and is pci-e 4x. I plugged that into the single pci-e slot on the mobo and plugged in an old agp graphics card into the agp slot (which is why this specific mobo was key because it has both agp and pci-e he he he). I also had purchased a supermicro 5into3 bay enclosure for easy and fast removal of the drives should anything go wrong... not necessary no but its easier and with the case I put them into (ancient micron server tower that the entire top and sides had to be taken off in 1 piece to get to the inside) it was much better of an option than fighting with that lid... plus it comes with a (very loud) 92mm fan that blows cool air directly onto the drives themselves. I also bought some WD RE3 1tb drives (re=raid edition). They are more expensive but they are designed for raiding (villages and raping women and children...no not that kind of raiding!!!). They have 2tb versions labeled as RE4 if you need the extra space. You can use your current drives in most cases unless you have a specific model of WD drive then it will fail every time you boot. The entire problem is that some times when a raid card requests data from a drive it will wait 7 seconds and if it doesnt get a response it will start a recovery process ... which as stated above can take days to finish... So you need a drive that has TLER on it ... either by adding it manually (I forget how) or by buying a raid edition drive. I opted to go with the RE drives... that way I can send them back if they fail
You can use the old drives yes but just be aware that they have a higher likelihood of causing an unnecessary recovery to run.