Amazon delivers most everything free shipping (50 dollars or more) even deodorant. Can get most prescriptions drugs cheap and over the counter in HK, so no need to bring.
Bring over the counter cold medicine/Nyquil, whatever your favorite is, bring that, Amazon usually won't ship drugs overseas.
Bring laptop and nothing else, not worth it to use transformers and such. Yes, electronics is cheaper in the US, but you still need a TV, monitor, etc. buy local or as some suggested UK Amazon if you can find it cheaper.
No import duty in HK (that I have ever experienced, packages not held up in customs). So ordering online and shipping to HK is really the way to go for everything.
For your initial trip moving over here, you're likely to need most of your carry-on allotment for basic and personal stuff. If so, I wouldn't worry about what you can save money on, but focus on what you really want and/or can't find here.
So, I'd start with the stuff you already have that's not worth the expense of replacing over here and/or that you really want. Then I'd make a list of the stuff that you regularly use and will need to replace between now and your first trip back home.
Then I'd research online to see if any of those are not readily available here or not easily ordered online from overseas. From my experience, the stuff I ended up refilling on each trip home was food and toiletries. But that gradually got whittled away over the years with websites like iHerb and Amazon.
But after a couple of decades here, there are still a few toiletries (skin cream, deodorant) that I still physically bring back, as haven't found them online nor anything comparable here that I like as much. So, I would think about those basics, find any that can't be had or easily shipped, and bring enough to carry you through your next trip home.
That said, if you're not aware, there are forwarding services from the States that are very cheap. I use buy@ndsh1p_today that only charges USD3/pound to forward. So, if you really can't find something here or online, you could have someone back home buy and ship it to your forwarding address.
Another website to take into account and that you'll want to familiarize yourself with is Taobao, as you can get things ridiculously cheap from China.
Lastly, I would just echo what someone said about shoes. I've never really enjoyed the shoe-buying experience here. They don't tend to stock half sizes, stores can be small, salespeople pushy and/or unhelpful, styles not to my taste, etc. And I don't really like buying them online, unless I have some reason to know they'll fit. So, I just can't be bothered, and have tended to buy them on trips back home, even if they cost more.
The shoe comment is an excellent point although I tend to buy mine through amazon.
American seasonings such as Old Bay are another thing to consider. When I first moved here I had a hard time finding less mainstream non-Asian spice blends such as ras al hanout, vadouvan, or zaatar but M&S started carrying most of these so no worries there.
Might want to check if clothing brands that you fancy exist in HK. For example Banana Republic doesn't exist here and brands such as J. Crew have since exited the market.
Mainstream spirit brands such as Jack Daniels are readily available but less mainstream brands such as Basil Haydens or Whistlepig are harder to find. Fortunately I can usually get Bulleit Rye at Watsons Wine.
Just a thought -
Do not ship any furniture over. When you do get here look online on this site and facebook groups of the area to find really cheap or free furniture, kitchen appliances ets. Many people leave especially over the summer and liquidate everything before they leave. It seems to me that the numbers of leavers has really accelerated in the past few months. Also shipping costs have skyrocketed so people are not shipping house contents like they may have before.
I see no one is recommending the OP can purchase stuff at the rather expensive American supermarket in Stanley.