I've moved a lot. Sometimes in 5 suitcases for the 4 of us, but when I moved to Singapore the company paid to move me, so I shipped everything I had at the time (6 boxes air freight, and I didn't take furniture, so nothing by ship.) Coming back we shipped the lot by ship, but I had a spreadsheet to tell me what was worth bringing and what was cheaper to buy again than ship.
First, practically, Don't take anything winter - it's 30 degrees all the time, there is no winter. Do take a jumper or two, as the shopping centres/offices are all very airconditioned and you feel chilly. Singapore is great - you'll be able to get anything you need, I didn't feel that I was lacking anything there from the UK.
When it comes to moving, it depends a bit on you.
We've got into a routine of taking only the stuff that we can't buy again in Ikea, and we have a shopping list of stuff that we just go to the closest Ikea and buy. It's about 3.5k for us to furnish living rooms/bedrooms/plates etc. We then donate the stuff when we leave. Did this in Singapore for furniture (At the time, delivery wasn't expensive, even the Market place stuff could be delivered, and they'd assemble it for a reasonable charge. Anything you had to have then, Sing Taxis have enormous boots, so I brought a lot home that way.
BUT if you can't live with Ikea stuff, that won't work for you.
If where I'm going doesn't have Ikea, then I rent furnished.
Also, storage is surprisingly expensive - we currently have a locker full of our stuff waiting for us to find a new place in our new country costing us 400 Euros/month - it's very annoying - so if you have a lot of stuff here, it still might be cheaper to ship it.