The only mechanical means of sorting that minecarts offer is by mass (and, even then, it's not the best). If you want to sort different kinds of objects apart from each other, you'll need manual labor involved to do sorting. Sorting into carts is pretty simple to do with manual labor, even from a single unified stockpile; you can just set the filter from the stop's settings ([ENTER] key).
The biggest obstacle that I tend to face when getting carts set up is just getting the track all set up. In any practical setup, you need to have a route on track from point A to point B; this applies regardless of the guide/push/ride selection.
After knowing the basics of implementation, you have a decision to make: how everything will be powered. There are two main types of minecart networks (guided and pushed), while the latter has three additional classifications (roller, gravity, and impulse). If you are just getting started, I would suggest a guided setup; this means that the track only needs the actual path and (possibly) stops; it doesn't require rollers or means of controlling what way carts move. The downside is that you need a dwarf to push the cart along the entire path, and it is limited to the speed of the dwarf. However, there is almost no risk of danger to others around (the biggest issue that exists is job cancellation on a slope).
Pushed, or "powered", setups don't require constant attention from a single dwarf. However, a lot more care needs to be taken into their planning. The actual way carts move will be dictated not by the route set up in the [H]auling screen, but by the actual pieces of track on the ground. Additionally, carts might be moving very fast, and so pose a safety risk to anybody nearby.
Personally, I stick with guided routes whenever possible, going into pushed systems only when I need to collect fluids or restrict the passage of dwarves across a stretch (like a restricted, vampire-only strand extraction area; you don't want to mix the populations, and you don't want the hospital or craftdwarves taking the extracted but unsmelted strands of metal).