Speaking of storing cars in general, and Healeys in particular, I have some considerable experience in this. Of course my observations and experience are strictly anecdotal -- no scientific instruments or lab testing involved -- but FWIW, here I wot I learnt:
For short-term storage of, say, a year or less, almost no prep is required. Sure, you should remove the battery (or at least disconnect it or turn it off), but that's really about it. If you want to increase the chances that your battery will still be good a year later, put it on a trickle charger. If you're really conscientious you can also move the car slightly to help prevent tire flat-spotting, but I've never found flat-spotting to be a problem if the tire pressure is up where it should be. Of course, you could just park the car and then start and run it for several minutes every week or two, and move it slightly each time.
For medium-term storage of, say, 1-3 years, I would write-off the battery; just remove it and give it away or recycle it.
For long-term storage of, say, 3+ years, you are asking for trouble unless you regularly tend to the car and can start it periodically. Seals and gaskets will dry up and begin leaking, and the brakes will likely be shot and need a complete overhaul. Then there are the potential problems of insects and animals moving in if you're not around to tend to these things.
Much has been written on this subject, but based on my experiences, there is relatively little you can do that will make much difference if you don't regularly tend to the car. Start it and let it warm up to operating temp regularly, move it slightly, pump the brakes, run the accessories, honk the horn! Only exercise keeps you, and your car, young.