Nona: That bike is trash. It is trying to have a million features at an extremely low price. If you really must buy a Walmart bike (they're terribly assembled, mostly) if you buy something with no suspension it may have essentially functional components.

OP: In your price range, shopping new, you're going to be looking at hard tails. Most will be basically modeled after cross country race bikes with about 100mm of travel and mostly 29" wheels and will have relatively fast steering which makes it easier to hold a line on slow climbs. There are also some bikes around that range with slightly more travel (110-130mm) and frequently 27.5+ tires that will still be pretty versatile on mild terrain but will be more stable at speed and will handle rougher terrain better. At a slightly higher price point you'll see some of these with dropper posts, which really are very helpful on technical terrain. Either a more XC or trail hardtail type of bike will work well for everything you've mentioned, but personally I'd recommend something more trail oriented, particularly since you can always use your old Nishiki for paved paths and gravel roads.