I would do a round table.

I would also do round. The eating area in our kitchen is almost 12x12, and we have a 42” round table that works nicely.

See if these links are any help.

https://www.houzz.com/discussions/921263/what-size-dining-tables-work-well-in-a-12x12-dining-room-round-recta

https://www.houzz.com/discussions/6279260/what-is-largest-size-dining-table-i-can-have-for-12x12-space

ETA - Our 42” table has a 20” leaf that’s rarely used.

a 60" square table only accommodates 2 people on a side. If you select a round table you can always have one that will take a leaf to enlarge the table.

I like the idea of a square table that can seat 8. I am not sure if your space 12 by 12 can pull it off but I find sitting at our square table for 8 is great for conversations.

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This is great if you need a cozy setting

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Round table with leaves so you can expand as needed. We have a 12’ square dining room and use a round table unless we have company.

Wow, thank you for all of the responses! And I'm not sure why I didn't see the previous threads in my searches. I thought the square would be good for conversation but I was worried it would fill up the space too much, and round would be much easier to find!