My bf and I moved in 3 months ago while also moving 2000 miles. It's an exciting time! (Not so much the x-country move. Would not recommend.) We were both coming from roommate situations so we ended up with an odd hodge-podge of household stuff. Fortunately there wasn't much overlap, but there were things we were missing...not sure if that's how it will work for you.
If you do feel like you're missing things, I would advise to wait until you see how what you have works in the space before buying things to fill in the gaps (meaning mostly functional). E.g if you don't have a couch, wait to see how the things you have fit in the LR before getting one. Goes double for storage. Generally to save space you'll want tall bookshelves, or maybe a cupboard with doors for hidden storage if there aren't enough closets. But you won't really know where this will all go unless you're already living there thinking "I wish I had storage here" or "I wish I had a surface to set things on, here."
Generally speaking, you want storage *everywhere*. Put things under the bed in totes, bags, boxes, etc. Coffee table with drawers. Storage ottomans. I loved my former roommate but she had a penchant for antiques and we had an old radio, a sewing-table turned side-table, an old card catalog on tall legs, a surfboard coffee table...there was literally no storage in the living room, even though there was furniture everywhere. I would have liked a place for movies, books, and games. She thought it would look cluttered. I didn't use the LR much if I wasn't having company, so I didn't push it.
Honestly, I think 630SF shouldn't be too bad for 2 people. We have 744 and it feels HUGE...