What type of wood would be best to make stickering pieces? Should they be round or square or triangular shaped?
Any pale-coloured hardwood is ideal for stickers and if the intention is use them repeatedly straight-grained pieces without many defects should be selected and the wood should be heartwood only. If drying softwoods a softwood species can be used for the stickers as well.
There's no advantage to making them triangular in section (and some obvious disadvantages including the corners being prone to damage) and square is much much easier to form as well. Square (rectilinear) is all that's used commercially as far as I'm aware which probably tells us all we need to know.
As there is a lot more to air-drying wood than sticker type, much of it not immediately obvious from looking at photos, it's likely you'd benefit from reading through a thorough guide to get up to speed and avoid a few common pitfalls in creating your stacks. The best guide I know of is published by the USDA's Forest Products Laboratory, Air Drying of Lumber.