Sons of the Republic of Texas seems to carry a bit more prestige than the Sons of the American Revolution. Harder to get into is the Society of the Cincinnati (members generally must descend from an officer who served in the Continental Army or Navy for at least three years, from an officer who died or was killed in service, or from an officer serving at the close of the Revolution. The tricky part is each officer may be represented by only ONE descendant at any given time).
I suggest you go to a local meeting or two with each “lineage society” for which you are eligible and see who YOU would like to hang around.
One thing about these societies is that I’m not the kind of guy that will dress-up in period costume and reenact battles (though I wouldn’t mind picking up some blackpowder firearms). I know the SCV does this alot. I’m more interested in the genealogical/historical resources and instilling an appreciation for history in my kids.