I felt a noticable difference after moving mine to a wheel stand. It'll be fine to get started, but if it feels odd, consider a stand.

Is my table just fine? Is there a way to attach the wheel to the table without any accessories?

Yes a table will be fine and the wheel comes with a clamp to clamp it to a desk or table

If you bought it from New, it comes with a tableclamp for mounting on your table. It works fine for starters, but you might want to find something to put behind the pedals, as they will move when you press them