Raspberries are some of the easiest plants to grow and get fruit from in northern zones. They produce heavily and are super hardy. To give them a kick start into the spring and producing for me I usually give them some spring care to get them going.
Mulching the base with grass leafs compost and wood chips helps feed the plant and hold down moisture.
One of the toughest parts about raspberries is they sucker and spread quite quickly. One easy way to keep them at bay is to cut them down regularly with a lawn mower. Alternately what I might do is put a physical barrier so they cant come up. Some landscape fabric and flag stones will do the trick.