OpenWrt 15.05.1 ("Chaos Calmer") is stable, and quite secure as shipped. Using the default packages, or a few well-known packages as add-ons will be fine from a stability, security, and UI standpoint.
OpenWrt Trunk ("Designated Driver") development doesn't seem to be going as quickly as it was before LEDE split off. It's still a development trunk version, and not guaranteed to be stable.
LEDE is just getting off the ground. Its nightly builds change (improve) rapidly, but you may not want your family (spouse, kids) to rely on it right now. It will have the same (or better) stability, security & UI characteristics as 15.05.1 when they ship their first stable version. There's no schedule yet, but look for an announcement in the new year.
For your stated requirements, I would recommend (and am personally running) OpenWrt 15.05.1
