The seismic response coefficient (Cs in ASCE 7) is a good place to start. For example, if your Cs is 0.07 and your DL+SDL=60 psf, you can approximate using 0.07*60=4.2 psf. This doesn't account for a lot of things (like facade loads) so you might want to use something like 0.09, which will get 5.4 psf. This will get the seismic base shear. You can run a quick calculation to get Cs using a spreadsheet; it's just inputting a few values, like importance factor and R. Or you build a library of a bunch of Cs's you get from similar buildings based on experience and just use that. I prefer to calculate Cs because it's very quick and low effort, but sometimes for a back-of-envelope type of calculation, I use a typical Cs (slightly increased for facade loads) times building footprint times number of stories times total DL, ignoring things like setbacks and balconies.
Distributing that approximate base shear is a different story. I've never needed to approximate that, so I don't have a rule of thumb for that. I only use it to check the base shear of my FEM model.
Of course, like with any rule of thumb, there are numerous caveats like when you have significant live loads that need to be included.