My only recommendation would be to try the crankset with a new chain and freewheel first. For the cost of it I would buy the new freewheel at your LBS. (You'll need a freewheel tool andway and if you take in your wheel they'll likely put it on for you).. The one caveat... what is your rear spacing? If it is 120mm the 6 speed freewheel will be two tight. You will need to respace your hub and redish the wheel. This is a chain of worms but worth the effort so you are not stuck with the old freewheel.

The veloce crank is a good buy, you may not even need new derailleurs, the PC58 chain should work good but in my opinion shimano chains are better than sram hands down.

If the derailleurs you have do not work well, first I would try picking up a late 1980s-early 1990s shimano mTB derailleur for the front, anything with the word deore in it, Some exage stuff works well too. And with derailleurs... same era, shimano 105, 600, RSX etc.. are all good, you'll save yourself some money and have nice shifting. One other thing, the chainrings on the veloce cranks are thinner, they will wear faster.