a) Temperature / climate would be my first point of decision. Lemons in general need more warmth than large areas of NZ can provide. So hence the major lemon in NZ is a lemon crossed with X (we don't really know, but some kind or orange), and is called the Meyer lemon. This can handle the cold far better than other lemons.
All the other lemons, like Ben Yen and such (it is the only one coming to mind). Need warmth. So unless you are in Auckland, Northland, BoP or in a warmer micro-climate I would stick to Meyer, irrespective of soil conditions.
All non-meyer lemons are actually budded onto trifoliata rootstock, so of these non-meyer's soil condition does not make any difference.
b) When do you want to use them? Most people want a lemon for cooking / drinking purposes on a semi-regular basis. Therefore you want a lemon that has fruit in all stages of development all the time. Again meye suits this, as is blossoms multiple times a year (I think it is just whenever it is warm enough). But most true lemons they call come ripe at whenever they come ripe.
You can also find more about the lemon types at Cooperfeilds web site., lemon information here.
Lastly I would not get a variegated variety (I did) these have less green in their leaves, so struggle compared to the non variegated types. So unless you have ideal conditions (which it doesn't sound like!) then better to go more vigorous.