How important is a Range Hood?

[Leonard Holmes]

We recently closed on our first investment house - an REO that had the HVAC stripped out at some point. We got a pretty good deal, and we are beginning renovation. It appears that there has never been a range hood for the stove. The house had gas at one point, but more recently had an electric stove. The ceilings in the kitchen and some other rooms have greasy stains that required extra prep work when painting. I think we probably need to bite the bullet and install a vented range hood, but the installation for this is pretty expensive. Is it worth it? Have others done this? If we leave this off (we bought a new electric stove) are we setting ourselves up for problems?

Leonard