harriet Moved last year to current property, about half/two thirds the size of where we were living before.
The minimalism approach makes a huge difference, as you'll already be in the right mindset for downsizing. The short version of what we did (huge open plan 1 bed flat with massive utility/storage space, to a compact 2 bed - 1 double, 1 single - no utility or storage): only very necessary or loved furniture - bed, two small lovely side tables, a retro shelving unit, an old rocking chair, 2 small bathroom organisers. These all flat pack/fold though so easy to stash if needed. Only necessary/loved appliances: kettle, toaster, smoothie maker, coffee machine (we do use them all!). Best pots and pans. Only enough crockery - 2 of everything per person, ie plates, glasses, mugs, bowls. Ditto with cutlery (though we have a ridiculous number of teaspoons 
). Basically repeat with absolutely everything!
Likelihood is, especially if you're buying and therefore likely to live there a while, you're going to end up buying stuff new/second hand as previous furniture may not work in the space. In our case (a bit different because we moved into another rental) that surprisingly only meant a wardrobe, a TV unit and a sofa (all of which were provided by the LL). I've got rid of so much and still going, so you come to realise how little you actually want or need.
My other tip is not to buy anything for the new place, as far as is possible, because you don't really know what you need or what will be best until you've got to know it. Have your basics - beds, sofa/s, a table, that kind of thing - and see how you get on. Even if you look at it and think, "This could do with a different wardrobe/dining table/bathroom cabinet", just wait and see. If you find yourself constantly saying to yourself, "Gah! We need a new table!" then you know it's time 
Also, prepare yourself for moving as soon as possible. That means sort through all your stuff as if you were moving tomorrow (this is actually what we're doing now even though we're not going anywhere yet!). Of course you can keep a maybe pile, for the stuff you're really unsure about, but start looking at each room and think about what you'd actually take with you. Anything that you wouldn't take can go now (or at least, if you prefer, find out if any friends/family/local charities would take it).