Can I use tubeless tires on Araya DM-27.5 Black 32 hole Rims?
A quick google search for that rim suggests they aren't marketed as being tubeless ready (normally, this is a point of advertisement for a manufacturer). So, you're stuck with running tubes unless you try a Stan's no-tube kit (video; or similar) or  ghetto tubeless (or the alternative method), but this is highly YMMV/at your own risk, and highly dependent on your rim+tire combo (not all rims and tires will work). Or get wheels which are tubeless compatible. Tubeless isn't cheap, but the advantages/disadvantages have been extolled extensively elsewhere on this SE and on the internet. 

As for punctures, you can make sure your tires are properly inflated, buy thicker/tougher inner tubes (thin tubes you buy may be under 1 mm thick; thicker tubes may be 4 mm or more, for thorn-proof tubes), run a sealant like Slime, and pick a tougher tire.