In regards to "accepting installation on my system"... I'll go with Emsisoft and BitDefender.
In regards to "trust", I chose "none of 'em"...
The proof is in the pudding people. Not one of us has one and only one security software application installed, or just one package installed that combines anti-[x], firewall, virtualisation etc... If we did in fact have one and only one, that would justify the "trust" statement. We all have our favourites, and then come the 2nd opinion/on-demand scanners, and then come the "better be safe than sorry" set of 3rd scanners.
Logic dictates placing trust in these apps is a recipe for disaster. However, believing that the application one uses actually works and does what it is designed to do (without transmitting your life story to the applications favourite CDN) is a mountain that is easier to conquer.