You need the needles/hooks that will give you the gauge needed for the pattern which may not be the same as the size used in the pattern as your tension could be looser or tighter. So work up some samples for your patterns with the closest sizes you have and see how many sts you get in 4" compared to the pattern gauge. Here's a needle/hook conversion chart
, maybe that will help you sort it out.
On the yarn, I dunno. DK is a weight unless it's also a yarn brand and so is chunky. You'd probably need larger needles and hooks for the chunky weight yarn - what needle and gauge does it suggest?