I'll take a stab at this. First, we have to clarify what you mean by 'distributor' and 'coil,' They perform different, but complementary functions: the coil boosts a 12V current to 12,000 volts or more to fire a spark across a plug, and a distributor sends the boosted signal to the correct plug at the correct time to create combustion. Compression ignition engines, aka diesels, don't require either, but do require a complex fuel-injection system that performs a function analogous to a distributor, only using fuel instead of sparks. Most modern gasoline-powered cars don't have a distributor but still have a coil on each plug that is fired by the engine control unit, or 'PCU' (sometimes ECU or ECM depending on manufacturer). Unless you're using a seriously modified ignition system your Healey engine will need both a coil and a distributor.
British Wiring, I believe, provides wiring harnesses to most of what we often refer to here as 'the usual suspects.' Their harnesses are good quality; at least, I haven't heard of many complaints about them (occasionally, some wires may be the incorrect color, for instance). Another, perhaps somewhat better supplier is Autosparks in England but they are likely more expensive and shipping can be costly (esp. after US Customs gets their cut). Cloth-colored, or braided harnesses may be more correct in some applications--there's some disagreement about which cars had it--but will inevitably get soiled. PVC wrapped harnesses are arguably more durable.
Negative vs. positive ground is no big deal; some like negative because most modern radios, GPSes, etc. need it. There are a few minor 'tweaks' required, but they've been covered extensively here and elsewhere.
Edit: I sometimes try to disabuse people from thinking there is such a thing as a 'safe' automobile. Your are never going to be completely 'safe' while in high-speed motion in a metal can (for that matter, you're not entirely 'safe' sitting in your home watching TV). Historically, some brands like Volvo have claimed safety features but they are, more accurately, more crash-worthy. There isn't much you can do to make an Austin-Healey more crash-worthy, though a collapsible steering column may be one possibility. These cars were built before the notion of 'crumple zones' and other design features became common in consumer vehicles. If it was possible to make a 'safe' car there would be zero casualties from vehicle mishaps and, last I checked we're still losing upwards of 50,000 Americans a year in automobile mishaps (not counting cyclists and pedestrians).