Which would be the best beach to go to around Oct. 11? We are a family of four with a 23 year old girl and a 25 year old son?

As JamesA has said many times, October is a tricky month for beach weather. The rainy season switches from the west to the east. Take a look at weatherbase.com (Kathie's favorite) for rainfall amounts.

which beach tends to get the least amount of rainfall in October.

Weather doesn't change on a date, the first week of October would not be so different from the last week of September, last week of October would be similar to early November.

It is when things change.

To give you an idea, these are rainfall stats for Sept / Oct / Nov:

Bangkok : 12.6 / 9.1 / 2.3
Pattaya: 5.4 / 9.5 / 2.8
Hua Hin : 5.4 / 10.5 / 5.2
Samui area: 7.6 / 9.8 / 5.6
Phuket area: 16.5 / 12.0 / 8.2

Look at Oct in the middle and you see the variation.
You can see that saying which one gets the least is pretty much impossible, if you are looking for a busy and lively place then Samui would be less than say Phuket, but by not enough to swing a choice one way or another.

Let's look at it another way - OK we need beach, now what other interests and activities ?

If we can add in those 'other things' then it then helps to make the best choice without sticking just on the beach situation.

So, shopping, restaurants, entertainment, treks, elephant rides, temples, soft adventures ?

Now resort, top class beach resort, mid 3 star range or budget.

I think if you can fill in those it can easily produce the best place, the weather is something you chance so perhaps wise to choose a place where there are other things to do, spend time shopping, spa, or simply releaxing, a good starting tip is perhaps to choose a place not quiet and stay at a large resort hotel, that way you have more facilities if it rains and also more things to do.

Of course you could get solid sunshine and not a drop of rain ! But who knows.
This year May was a really bad month for rain, but it can vary.

This gives a 30 second intro, fast and easy just to get those place names in mind.
http://www.beachsiam.com/where_to_go.html

JHust to add if you want a lively island with that age mix it may come down to Samui or Phuket if you want lots of tourist things, but I would have a family chat and you might want to add in say 2 places, if you are on a 2 week trip, split it, get 2 chances, try one place one side and then the other side ( 2 different weather patterns ) so you at least increase your chance.

I jyust say your other posting and say it is just a few days at the beach after Bangkok, in that cose I would think about if you want to fly somewhere for those few days or just head to a beach by cab from Bangkok.
If it's just for a few days I would perhaps say head so some nice resort with good poolsd at a beach close to Bangkok like Hua Hin Cha Am area if it's just for a few days