I’ve moved internationally six times for school and work, so have been in the situation of packing for a six months to a year in two suitcases, or packing in two suitcases for several months until the rest of my stuff shows up.
Others have covered a lot of my advice, but I’ll add a couple of thoughts.
In addition to putting small items like socks/underwear inside shoes to ensure I’m not wasting space, when packing shoes or other large/inflexible items, I usually don’t put those items directly on the bottom or wall of the suitcase, but rather put clothes underneath the shoes/large item so I don’t waste any space. The shoes can push into the clothes below/underneath them and don’t leave any gaps, if that makes sense. I also make sure to put clothes in/around the gaps between any of the bars from the frame/handle inside the suitcase to make sure I don’t waste any space.
I usually don’t use packing cubes or compression bags, because I find that those make it harder for me to use all of the space in the suitcase and compression bags can end up causing you to go overweight easily. Though, if you have something large/puffy but relatively light like a puffy jacket or pillow, I could see how a compression bag might be useful for that type of item.
As others have said, a luggage scale is helpful. Weighing every item is probably a bit much for me and I’ve done this enough that I can usually guess the weight of my suitcase pretty accurately, but I absolutely use my luggage scale as a sanity check before heading to the airport.
Another poster shared their experience of one of their bags not making it to their destination the same time they did, and I had a similar experience arriving at one of my study abroad destinations, except both checked bags didn’t make it the same time I did (though both turned up a couple of days later). So, I now always pack anything I need for the first 72 hours or so in my carry on.
You’ve probably also already considered this, but if you take any OTC or prescription meds or like to have OTC meds on hand in case of illness, you may want to bring a robust supply of those or at least investigate whether the same medicine is readily available there. I’ve found that I am least inclined to deal with the adventure of foreign medical systems and pharmacies when I’m not feeling well. I prefer to bring OTC meds I’m familiar with (and familiar with how they’ll affect me) to have on hand for such occasions. While studying in Australia, I ran out of the cold medicine I brought with me, so went to a local pharmacy. The pharmacist looked at the empty U.S. medicine box, handed me something and said it was basically the same. It was, but with codeine, which they sold OTC there at the time. Fortunately, no harm, no foul, and I just slept more than I might have with the U.S. meds, but it was a lesson in differences between medical systems, even where care is on par with/better than in the United States.
This is less packing-related and more getting set up in a new country-related, but for my last couple of overseas moves, I’ve planned an order or two of stuff from a local online retailer (local Amazon, a local pharmacy/drug store, etc.) to arrive a few days after I do. I do recognize that students don’t have the same budget that I do now that I move for work, but given how precious space/weight will be in your suitcases, it is really worth looking at what is worth hauling over vs. what you can order easily enough to be delivered to you after you arrive. Plus, saves me the trouble of scrambling to find stuff in unfamiliar stores while jet lagged. Moving for school/work is not the same as traveling on vacation, and you’ll have two years to enjoy investigating the local stores near you. So, it may be worth springing for an Amazon.co.uk Prime or similar service subscription and just planning to order yourself some of the stuff you’ll need to arrive a couple of days after you do.