I would not recommend a 1-wire alternator as its responsiveness to the changes in electrical demand is less than a 2-wire alternator. Also, a 1-wire alternator is more expensive and, as a specialty item, will be more expensive than its standard 2-wire counterpart. Additionally, the installation of a 2-wire system is not difficult and make up the overwhelming number of Healey conversions with a massive amount of experience and knowledge held by members of the BCF alone. Last, you charge light will work as usual.
As far as the choice of alternators, the commonly available Delco 10SI (65 amp max output) remains your cheapest choice with Japanese alternatives coming up because of their small size. Mountings range from a specially casted side plate from Denis Welsh Motorsport on the very nice but expensive side, Hendrix Wire Wheel for a complete alternator conversion kit, to a DIY at the least expensive end.
As an example, I chose the DIY approach at a total cost of $70 with a Delco 10SI 2-wire ($35). Adding a double pulley at $15, I was able to install Delco on my existing generator mount with the use of 2 washers, a 4”+ piece of pipe to take up the space between alternator and rear engine mount ($4), and a long bolt ($1.20). A universal adjuster was purchased ($15), cut down to fit, and mounted on the opposite side of where the original adjuster was mounted.
Although others can provide additional alternative approaches, please keep in mind that each commercially-available mount will support specified alternators. Also, keep in mind there are differences, among Healey models, in generator mount spacing (generator length) and placement, as well as pulley V width. When choosing a more modern alternator, make sure you can get and install a compatible V-pulley.
Hope this helps,
Ray (64BJ8P1)