The dissolution and consequent buffering capacity of crushed coral is minimal. If the crushed coral you are sold is actually crushed coral and not calcite, you will have a slightly better dissolution, but the overal contribution is negligable. Another thing to consider is the coarse natire of crushed coral and it becoming a detritus trap, which WILL lead to dissolved organics and nitrification favoured over denitrification due to greater depth of sand needed for denitrification with coarser substrate than with fine and more evenly round shaped sand.
Although live sand has some small benefits, it is hardly worth the initial setting up expense. Fact of the matter any substrate added to your tank will eventually become live. The biggest advantage of adding entirely live sand to your tank, is its potential to significantly decrease the cycling period. Again, hardly worth the expense, as learning some patience early on in this hobby is paramount, and / or, there are other ways nowadays to cycle a tank within two weeks.
Pool filter sand is hardly as white as the sand found around most reefs from which we generally keep specimens, but if you are happy with the look of silica sand in your display, by all means, its your tank. Just be sure it is inert sand with NO possible contaminents.
A fine layer of proper aragonite (fine crushed coral) in your display is best imo and use inert silica sand if you MUST run an in sump DSB. Minimum depth depending on sand from 15cm upwards for it to really have a beneficial effect in terms of removal of nutrients from the water column.
In the past quite a few reefers from SA used reggies play sand for dsbs, perhaps something to look into.
Perhaps consider the more popular approach nowadays of a bacteria and organic carbon source run tank.