I'm the youngest of 5 myself, and what my Mom did was give in to it.
She bought about 10 inexpensive cotton table clothes and made a rule that whoever cleared the table after supper took the table cloth off the table and put on a new one on from the stack of them in the side-board. We then had to just put it with the laundry, and they got washed with the dish clothes and towels.

I don't remember them ever being too badly stained, which is some kind of miracle between 5 kids eating spagetti and the fact that my Dad's special talent was for tipping over beverages. (He did it every night for a month once. It was never intentional, just one of those things.)

We have two oilcloth table cloths - and they're great. Nice and durable, and they wipe down incredibly easily.

Our ones are Cath Kidston ones.

EDIT: My wife has informed me that in the US this is also known as "American cloth".

Have you considered getting a glass top for the wooden table? That is what we have done. We got safety/toughened glass. We got it from a glass company over 5 years ago.

We don't normally use a table cloth. I just wipe down the glass top after meals. You do have to occassionally clean under the glass.

It copes with hot drinks but I use mats under dishes out of the oven. Our glass has survived a couple of moves.

I got a flyer in the mail today from Bed Bath & Beyond advertising a new type of table cloth made out of water bottles! Sounds intriguing. They come in multiple sizes at reasonable prices...plus you can use a coupon. :)

It advertises that liquid spills bead up, but solid messiness may be a different story, I donno.