72" round or 76"x42" rectangle

You need at least 24" elbow room wide for each person. You need at least 3' from table in order to pull back a chair and get up from the table comfortably.

A 5' square table should do it, as in 5' plus 3' (all around) = 8' and you have 12'. 2 diners each side. Perfect! Choose a pedestal base, not one with corner legs.

That will leave you a 4 ' buffer, with chairs pulled out to add a narrow console table for serving...which would come in handy

You would need a 80 inch round table to seat 10 people comfortably, and adding three feet all around for chair space, your room is not wide enough.

Furthermore, there is a tremendous amount of wasted space in the middle of the table.

A rectangular table 96 inches in length will seat 10 comfortably with 4 on each side and one at each end. You don't need to get the table that is 96" long, just get a table that has two leaves, and with the two leaves added will be 96" long.

At 96" it will extend beyond the strict length of the dining room, but it is not a big deal for the table to extend past the doorway just for the duration of the meal. After the meal is over, you will take out the leaves and the table will be short again.

It is most important for your guests to be comfortable while dining.

You also want the table to be sufficiently wide, try for a table that is 45-48 inches.

Any narrower than that and you may not have sufficient room for serving pieces, centerpieces, candles, etc.

This is especially important when you do not plan to have other furniture in the room such as a buffet.