Riding mountain bike to work regularly?
It's hard to get a better bike than a mountain bike for going up and down hills.   Even a cheap one.  The geometry is set up so it's controllable both up and down steep hills, and the gearing almost certainly goes low enough that you'll be able to pedal up even the steepest of hills (as long as you're strong enough to push the combined weight if you, your bike, and all you're carrying up that hill...)
For going down steep hills, as long as you're not trying to set any speed records you just have to be able to stay in control.  (I'm ignoring brakes overheating on long descents here...)
For going up steep hills, as long as the bike is geared so you can pedal it up the hill fast enough to stay upright, the only thing that really matters is the combined weight of the rider, the bike, and everything else you're carrying.  Shaving weight off even the cheapest and heaviest of bicycles won't make a huge difference here, and even the cheapest, heaviest mountain bike probably has low enough gearing.  Shaving just 5 lbs or 2 kg from a bike can get expensive.  The easiest place to lose any weight is to not carry anything heavy.  The next easiest place to lose weight is you...
One thing that can help is using either toe clips or clipless pedals to allow you to also pull up on the pedals.  That will allow you to engage more muscles as you climb and that could help take some load off your quads and glutes.  Note, though, you'll still have the same cardiovascular limits on how much total power your muscles can produce.
Finally, though, it's all about you and your fitness and strength.  Those will both improve as you ride more.  The ride will get easier and/or you'll go faster.