Ideal situation is to have all flights from point A to your final destination on one itinerary, even with different airlines involved. If there is a delay or cancellation of a flight, the airlines will re-route you. It may be inconvenient, but you will not incur additional charges. One itinerary is not always possible and separate tickets may be much less expensive.
If booking separate tickets, make sure you leave enough connection time between flights – this applies to your inter-island flights too. There’s worse places than HNL for a long layover, but if you have missed your connection (your fault or your arriving airline’s fault), the departing airline will have little sympathy for you. They will charge you a change fee plus any difference in fare. If you have booked round trip inter-island airfare, make sure you call the airline if you know you will miss the connection, otherwise they may cancel the entire booking including the return leg.