I'm probably the wrong guy to ask what charger to buy for reliability sake. My Schumacher that I currently have has worked for almost 3 years. Usually, something goes wrong about that time in my world. I can say tho if you are looking for a machine that has the additional starting circuit to buy and use wisely. Others may have different views, but for most small engine applications I wouldn't exceed 50Amp start circuit and to use that feature sparingly. You are better off charging the battery.
The charger you describe above doesn't have a starting circuit, but should be a good all around charger.

I bought a "Vector", "Power On Board" smart charger with 25 amp, 10 amp, 2 amp charging circuits, and 75 amp starting circuit. It is fully automatic and will recharge a car battery in 2 hours. It's circuitry varies the current and charges the battery slow or fast according to it type and size etc. It has modes for gel cell batteries, sealed lead acid batteries, agm batteries (absorbed glass amt), as well as wet cell batteries. It has an alternator check circuit and a battery voltmeter display. It turns itself off to. I really like mine. They are available at many places but the link below shows one at Sam's Club for $49.95. A good buy in my opinion.

Here is a link that might be useful: Charger at Sam's Club