Regarding what you need to purchase. Get a water regulator to assure you don't ruin pipes from a high pressure water source.
I purchased a surge protector to protect your rig from bad power sources. Most people get one.
Along with the sewer hose, we find a clear elbow very valuable. It allows you to see when the black tank starts running clear. Also get some tank treatments to eliminate bad odors and use proper toilet paper (there are lots of posts debating proper TP)
Get a water hose built for drinking water. (BPA free). Also a water filter to use before the hose. Some campgrounds have some pretty not so great water so it helps a lot.
I assume you have a 30 amp service for our trailer. You will want a step down plug for a 15amp outlet at home.
Keep the humidity down in your trailer by using dehumidifier tubs or a small dehumidifier if electric is available.
If you will be boondocking a lot (camping with no power available) you will want to upgrade your battery.
If your trailer will be sitting in the sun, I suggest tire covers to reduce UV rot on the tires. And watch the tire pressure closely to avoid blowouts. The ires are not great that come standard on trailers.
I have a fifth wheel so cannot comment on stabilizers and other towing safety needs. If I had a tow trailer I know I would have one.
I'm sure there is more, but this is pretty standard need equipment.
Have fun with your new rig