one sample t test (beta=0)

Hello. I have a dumb question about one sample t test.
If I want to test the hypothesis: beta=0 , what is the formula for the t statistic?

Is it: (beta-0)/(s/sqrt_of_n)?
or is it: (beta-0)/(sqrt_of_s)

The first formula seems way too lenient because your t statistic will always be significant unless your sample size is really small. But I guess it's not that urealistic for a beta to be always significantly greater than 0. I don't know.

I would really appreciate any help on this question!

Many thanks