Abus Bordo (Granit X-plus model, not the weaker one) is both more versatile for locking than a U-lock, as well as the easiest lock to carry of all the decent ones I've seen. Small frame mounted bag, or just a bag pocket - the lock is folded into a small "brick", not much larger than say two smartphones put together.

I leave a good chain in the place I park often and regularly, carry an Abus Bordo on the bike always, and occasionally, when going into high theft risk areas, add a good U-lock to the package (also Abus in my case).

It costs a lot to get good locks, but then you don't need to buy new bikes every year - lots of bike thefts in my city. Turns out cheaper in the long run.

Saddle, and other stuff are secured to the bike with bolts, or chains staying on the bike always.