It should be big enough so that when you pull out the chair to sit down it should still sit on the rug. Too big is much better than too small. No, the rugs don't have to match. Even though you can see the other rug it's still considered a separate area.

You have lots of rug options with that dining set. Something with a nice wide border. Any Oriental style would work.

I have 3 areas that can be seen from the foyer. I chose to have them all match in color, though different patterns. Some people would be ok w/o having the colors match, but i'm just a bit anal, or ocd....take your pick. ;)

The rug doesn't really have to be Oriental in style. Modern rugs are also very much in and there are hundreds of different designs. Your room so far is very neutral and I would be inclined to pick rather brilliant colors, but the rug could also have some beige in it to tie in with your beautiful dining set. A terracotta red would look great with the warm tones in your room, but there could also be navy, light blue, turquoise, yellow, beige and other colors. in the rug. I would then pick out some fairly large wall art that also contains some of those tones.

We're going with an Italian theme in our dining room. We just moved in but we already have some art for the walls. Great idea about bringing in some brighter colors tho. We have some turquoise and yellow going on in the room across from the dining room so it might tie it all in!

When you say "Italian theme", what do you mean?

This is some of the decor

And this

I like that one but with a little more color. ❤️

Are you looking to stay away from the traditional oriental style?

overstock.com has lots of rugs to choose from if you'd care to look there. Also paintings for that matter. Many drapes also should you need them.

Yes Overstock has tons of rugs and many are on sale now. I also would take a look a esalerugs.com They have some great rugs and a nice selection. Free shipping and free shipping to return if you do not like it. I have a couple of their rugs and really like them. They have held up very well. Here is a lovely one fro esale but they have a million others.