Are you talking about the big Healeys or the little (Sprite) Healeys?
Are you interested in concourse, or just a good driver?
A new plastic-insulated wiring harness with real crimped connectors will drop you out of concourse judging, but will make for a fairly reliable car. I drove my 1959 Bugeye for a decade without any electrical problems this way.
Join the club FIRST before shopping for a car. All the good cars are sold member-to-member. Healey people dont' want to see their "baby" go to some speculator.
www.healey.org/index.shtml It's a great club with a lot of elan and a very good monthly magazine.