Narrower doesn't always mean faster, especially when it comes to less than stellar surfaces. It becomes a bit of a headache but basically, wider tyres roll slightly faster on smooth surfaces, much faster on rough surfaces, but they also weigh more (can feel sluggish) and create more air drag (though very insignificant at the speeds a hybrid can go). You also have to consider tread design, the rubber compound, tyre carcass construction, inflation pressure etc.
If you drop to say 32s, the bike will feel livelier and accelerate a bit better, but it won't roll any easier and you will feel the difference in comfort. That said 32 is already quite wide compared to anything you'd find on a road bike so don't stress too much about it.
I've had extremely good experiences with Continental tyres, even their cheaper puncture protected models grip well and last an age. It sounds like you might want something with a bit of tread to help you out on the unpaved paths, but not so much to be a complete drag on road. One option is to have a semi-slick with a bit of tread up front where you need the most grip, then a complete slick or minimal tread up back where there's more weight and less grip needed.
I'm more familiar with 26" tyres so I'll do my best to find some recommendations for 700c:
Continental comfort contact I've used tyres very similar to this (Conti CityRide) with great results on mixed surfaces, the center smooth tread rolls great and there's enough side tread to dig in a bit and help out on the loose/soft stuff. Puncture protection is excellent as well.
Continental Travel contact I've just picked up the 26" version of this, not used it yet, though it gets excellent reviews. Same idea with a smooth center tread and some more aggressive knobs at the side. Maybe this up front at the comfort contact at the back would make a nice combination (I'm considering it myself for mixed surface riding).
A very popular option is the range of Schwalbe Marathon tyres. I don't have any experience of them though I know plenty here do - I see as I've been typing this the discussion has already kicked off!