Wheelbarrows are covered above. I happen to disagree with the above regarding minecarts though. They're some of the most fun I've had with DF.
They can also be the most annoying pieces of !@#!@#!!!! you'll ever argue with.
Minecarts are amazing little tools, particularly if you're doing significant work with small materials. I use a trackless minecart half the time. You can load them and then have one of your dorfs haul the thing at the speed of a sleeping snail to where you want it to go... but instead of sucking up 200+ dwarves moving those sandbags, you get one guy once a month dragging it down to the magma forge. Same again for goblinite cleanups.
Don't use minecart/quantum storage for food or booze, and bins seems to make a mess (for me) too. Booze is a significant problem, as dorfs will hang around at the minecart and their stubby little arms can't reach in for the booze, but they won't let anyone push it to dump it for them either, so they die of dehydration beating off their saviors. It's kind of funny but a bit odd.
You'd think you'd want to use minecarts for stone, but it's time intensive. You'd need a few (3 or 4) legendary engravers to really keep up with stone hauling via minecart if you're simply bringing it to a local mason/stoneworker. It's just not worth the effort for that, not for 5 stones and a deadly cart parading through your traveled locations if unguided. Go wheelbarrow.
However, I've about nailed down a magma-forge drop and cart return without power requirements for all my ore. That's been a personal goal and once I get it I think it'll be well worth it. Now, do I happen to have over 1000 bars of iron already along with other asundry bits from manual hauling... well, yes... but that wasn't the point. After 4 years my dorfs have barely made a significant dent in my ore hauling after I overmined the heck out of some veins. I'll let you (and others) know how well that plan works out.
As for bugs, wheelbarrows are pretty much foolproof. Occassionally some dorf sticks them, with the stone, into the minecart. When you dump the cart you'll get the barrow back but I recommend quantum rock stockpiles be set to guide at 75%, instead of 100%, because of that.
Minecarts are... well... they've got a few oddities. There's impulse ramps, water cannons, jumping magma mist defense systems, and a few other assorted things going on with them. A lot of !!science!! has been done with them.