Hey Anders,
Sounds like a cool project. Here's a few of things to consider:
If you are using pre finished counter tops (or pre sanded), instead of biscuits or sash clamps consider pocket screws and a Kreg jig. As much as the purist in me objects, there really is a place for them and it's the underside of your table. Be careful to place them so that they are well within the finished perimeter, and use glue. The advantage of the pocket screws is that you should get perfect alignment of the pieces so no, or minimal resurfacing once the glue dries.
Given that there is no apron, make sure that the frame is small enough to be unseen from standing height. It should be as big as possible given that constraint. The legs should be welded into the frame and if need be, gusseted for stiffness. It really depends on the size of the legs. A goodly sized square tubing might be able to do without gusseting, but I am a belt and suspenders kind of guy in this regard.
Fasten the top to the frame with slotted holes in the frame to allow for wood expansion across the grain. Don't ignore this or you will regret it.
Good luck, take pictures,
Tom
ps. If you have a router, consider using a 25º under cut bit with a bearing to create a slight bevel on the edge. It adds a little elegance and tends to hide any irregularities in the shape.
pps. I just took a look at the Ikea product which you linked to. I'm not sure the english site is the exact equivalent, but it shows a veneered particle board piece. You will need to protect the edge with banding or some other such treatment. Alternatively, you could go with a solid wood top such as
Boos Block. It's more expensive, but a better product and a better match for the effort that you're putting into the project.
_________________
"There is no path to peace, peace is the path."
Mohandas K. Ghandi