What is the best type of board for going miles out to sea? Just a regular strapped surfboard?
maybe look up that straight crossing with snicker sponsorship. they seemed happy with their gear.
What are you going to do miles out to sea? Just ride there? or surf bommies? watch the whales?
Firstly the smart arse answer, if you have to ask then you're not experienced enough to ride miles out to sea. 
In my opinion, unless there is something special out there to see or do there's no point riding way out to sea. The water is the same. The wind is the same. If you get any sort of gear failure you're pretty much ****ed. Rule one is to never go out further than you are prepared to swim.
Anyway, for light winds and long coastal cruises look at a kite raceboard. Massive upwind performance and they go in a seagull's fart. They are quite technical to ride and can be uncomfortable in chop. They can be ridden toeside but it's better if you gybe.
Twintips are easiest to ride and a larger board goes best if the wind drops off. Also you don't have to gybe or ride toeside so you eliminate that period where you might fall or lose your board. I find it very scary to fall or be separated from my board in open ocean. There's sea monsters out there. 
Strapped surfboards are great fun in big swells, not too bad in light wind and you can take your feet out of the straps to trim for better performance. The downside is that you have to ride toeside, which is very tiring on the backleg, or gybe and risk falling and getting separated from the board.
