We both slept really well that first night as the seas were calm. We were gently rocked to sleep and woke up refreshed. Although getting a cabin is a more expensive way to travel, it's definitely worth it for the quality of sleep you'll get. There are more budget options including reclining chairs and sleeping pods.
Another thing I would highly recommend that you do is to get up early in the morning and watch the sun rise over the sea. There's something seriously magical about this view, and if you're really lucky, coming into Aberdeen harbour you might be lucky enough to spot porpoises jumping in the wake of the ferry.
The NorthLink ferry terminal in Aberdeen is ideally located just across the road from the train and bus station, perfect for onward connections.
My son and I spent a very enjoyable day in the trees at the Go Ape facility just outside Aberdeen, a short bus journey away, before returning to the city centre for a spot of shopping and fast food (there's no KFC in Shetland - he wanted his fix!) before heading back on board to return to Shetland. By this time we were rather hungry after our day adventuring, and the chicken strips (for him) and Viking burger (for me) went down a treat. For afters, we both indulged in the chocolate marquise - a seriously rich and delicious chocolate dessert.