As I understand it.
Softmodding, stems from homebrew code so you will need to gain a copy of Zelda twilight princess initially. Come in two main forms, those being standalone and incorporated into the system menu (earlier versions needed a homebrew launching app, current versions can allow you to use your normal disc channel to do whatever).
Hardmod: now there are several types of chips.
Drivechips: these vary from the initial wiikey style chips (I know there were earlier ones) to later d2pro type chips as Nintendo changes the type of chip the drive used. You can swap back and forth between drives quite easily. The newest models are presently unable to be chipped and that does not look set to change any time soon, the slightly older ones Nintendo has made very hard for those new to the game to install unlike the first few generations which were trivial. There are some clip on chips but I am not overly enamoured with them (others swear by them though).
Drive replacements: these are very new and come in two main forms although they both install in the same way.
Drive emulators: Only the flatmii comes here right now, it hooks up to the USB of your computer and allows you to stream ISOs from your PC with the flatmii essentially being the new wii drive (although you can still use your existing drive at the "same time". Although it acts in a similar way to the methods below you will still need a chip or softmod to play burned discs in the drive.
Cable chips (I need a better term), for the most part I consider them softmod on a chip (same limitations and owe more than a passing nod in how they work as far as I understand it).
Re NAND: there are some early stage hacks and regarding size take a look at scrubbed sizes and take a bit more off for updates and the like. That is the real size of a wii game and there is some early stage work happening on the subject.
The "best" I would say is a hybrid between the two methods (forget warranties), long have we been able to use homebrew to boost compatibility and do other fun things even with commercial games.
Shopping list for the ultimate modding kit (I will leave out SD cards but you will want a decent sized one 512 is what I would consider using although you can use smaller).
Flatmii. Says it all really, this allows you to keep a selection of isos on a computer (often a few hundred megs each if you store them properly)
Drive chip (pick one, they all do the same thing and as I already mentioned software hacks can make up for any lack of updates bar GC streaming audio). You may have trouble installing one of these with a flatmii.
USB Gecko- not a necessity by any means but quite useful. The software counterpart (which works without the device albeit with reduced functionality) helped out rather nicely in the earlier times.
Also on the subject of homebrew a wired connection could possibly be handy at some point as wireless hardware and some of the linux based homebrew do not get along.
Softmod kit, many exist and most do the same thing. Others focus on or add customisation but I say spend some time reading up and customise by hand pulling anything from packs if that is what you want.
As mentioned you will need a copy of twilight princess to play this homebrew thing properly (although flatmii could take care of that), if you are still at an earlier menu (3.3v1 or below if memory serves) then you might not even need that.
Long story short you need to get the 3.2 system menu (all advantages of the later versions can be obtained)
http://wiibrew.org/wiki/AnyRegion_Changer for this. You may also need to downgrade your IOS if they have been patched (current softmod methods should take of this but I would do it anyway).
There is an app that should be coming at some point called bootmii that allows you to load code before the system menu and all that it entails, in the meantime there is an app called preloader that people are using in place of it (it is not quite the same but still very good and affords most of the immediate benefits for those of us in these circles that bootmii could)
http://wiibrew.org/wiki/Preloader
When it comes down to it softmods have a 3x read limitation (chips other than the cable chips have 6x) which can have an effect although recent versions of softmods are very good and you really need a stopwatch to tell and compatibility on one or two games is lower but they can usually be fixed.
I mentioned fixing, Nintendo try various things and people like to mod things; hardmods if done with good hardware can avoid most of it although I strongly suggest you know how to do it all anyway (IOS patching is the main word you want to know with wiiscrubber and multiboot being the others, there are some additional tricks you might want to know but save it for later).
The only other thing you might like is a NAND chip (to allow swapping around or switching), these do not exist commercially and short of proper electronics skills I would not suggest it. Advantages are negligible for most people (more NAND space = more wads and not much else)
