khuon

For your applications, I think you generally have five different routes to go.

1. Hardtail MTB - usually has front suspension with around 3" of travel, big knobby 26" tyres and designed more for offroad rather than onroad riding but you can always "trim-down" the tyres to semi-slicks to make it more road-friendly. The position will be more upright than a roadbike but there are different kinds of hardtails. I would suggest one that's designed more for XC riding than say a hucking or freeride bike.
2. Comfort Bike - generally very upright seating, smaller to medium sized 26" tyres with less aggresive tread patterns and may sometimes be equipped with a low-travel (around 1") front suspension fork as well as possible a suspension seatpost. These are not meant to go very fast or far. They will generally not have higher gearing or as many gears as other bikes either. They're basically multispeed versions of the cruiser bikes. They can handle very light offroading if need be. Some of these are also billed as "utility bikes".
3. Hybrids - sport 700C wheels with medium width (for roadbikes) slick or semi-slick road tyres and will sometimes come with front suspension although I personally think that for this type of bike, suspension is unnecessary and would prefer a carbon or high-quality steel fork. Sometimes they will also have a suspension seatpost too although I personally would prefer a rigid carbon post. They will position you in a lower more roadlike position that's fairly close to that of a performance XC MTB. These bikes are more road oriented but if you pick clean lines through very light offroad trails, you should be okay.
4. Cyclocross - basically roadbikes designed for offroad course but not to an extent of a full-fledged MTB. They will have wider 700C wheels with more aggresive treads than a roadbike. They will position you in a lower roadbike-like manner and have drop handlebars as opposed to flat handlebars of the other above bike types. They're usually made of high-quality frame material and don't have suspension. Unfortunately, most of these bikes are priced higher as they fill a much more niche market.
5. Tourer - very much a roadbike with longer chainstays and longer wheelbase to make them more stable. All components are heavier duty but also means the bikes weigh more. They have many of the same attributes as a cyclocross bike except they also have provisions to mount racks and fenders. They also have lower and wider range gearing like a MTB. They're designed for carrying a lot of load over long distances. Some people find they make excellent commuters too.

My suggestion would be to go out and test ride models of each of these types of bikes. Then you can start narrowing down specific brands and models.