What machines in a typical gym would help improve my strength with regards to lifting, carrying and so on? I take it I should be looking at improving muscles in my arms and upper back?
That machine is called a barbell and you need to deadlift it.
Deadlifting is not something you can start doing without learning it first, like you might with a machine. But no machine can teach to how to lift heavy weights without screwing up your back, learning how to deadlift will teach you exactly that.
Find yourself a powerlifter or trainer at your gym, have them show you how the deadlift works, and let them check and correct your form. The basics are easy enough to learn though, you can do that from a book or online.
Of course, you can deadlift anything you want, like kettlebells, instead of barbells. The farmers walk would be a great complementary exercise to the deadlift for your purposes.
In addition to the deadlift, you would probably want to learn how to sqat as well. Sqat is another great overall conditioning movement that will leave you feeling stronger and more capable at the end of the day. Deadlifting and farmers walks are a bit advanced, especially for someone who is not sure what a shoulder press does, be careful you don't injure yourself.