Bed Bath and Beyond is great because they offer a 20% off registry completion month, and you can buy things off registry too, which is nice. Unfortunately, they have changed their return policy so it's not quite as lenient, but they are still great to work with.
Register at Target, too, even if you don't give that registry out- you get a $20 GC for registering, and if enough people buy off your registry, another $20 GC after your wedding.
As for what to register for: we were very space-constrained, so we pretty much stuck to upgrading what we already had. Ex., we had an ikea dish set, but they were very breakable and the bowls got hot before the food did if you reheated in them. So we upgraded to the nice stonewear sets BBB carries- we love them, and I haven't been able to break a single one, even dropping one from a cupboard onto a tile floor.
We also got "back up" items- ex, I knew our flannel sheets were on their way out, so we registered for another set. Lo and behold, just a couple weeks ago they went out, and we replaced them.
We also got items that enabled further frugality, like glass snapware (no chemical leeching, easy to clean, bigger set = more leftovers!). If you don't have good kitchen foundation items, like good knifes, now is the time to get those.
Congrats on your engagement =)