If you want an more structured look, you can go for a square. But as Dohraime said, size is key! Colour wise, I would choose something that contrasts with both the floor and the table :)

looks wrong as it is currently - IMO it would look way better centred in height between ceiling and vanity and also possibly better centred to the basin, since it's offset to the vanity - a mirror centred to the vanity but offset to the basin could look odd - but it's hard to judge accurately from those photos as it's hard to gauge the scale of all the various elements.............like with everything to do with design it's always about balance

I think it depends on the size of your household and how many people sit down to dine. Do you have family and friends for dinner? The current round table looks like it can seat 4 people comfortably, but six people may be a bit cosy. If you need a table for more than four people then I would go rectangular. You could always compromise with an oval table? An oval table doesn't need to align with anything, so it can be angled to make the most of the space without looking crooked. Best of luck, Dr Retro of Dr Retro House Calls

Really your choice. But a posting a plan may get some feedback for your specific.