Nothing wrong with cheap bikes but don't expect them to do the "Ultimate" in their category well.

On mountain bikes- most of the cheaper bikes will do a bit of rough riding- but for the money you have to look basic. Rigid forks and "V" brakes instead of a POGO stick up front and disc brakes that don't work. Gearing is the other point. Most cheap MTB's never see offroad and in fact rarely see mud so they are set up with higher gearing for pavement riding.For offroad that will see a few trails up hills- then you will need low gearing. normally this is done with a crankset that has 42/32/22 crankrings on the crankset and a large rear gear of at least 28 teeth.

One thing you must do- if you want a bike that will last and be suitable for offroad- is forget about the "Wallymart" bikes. Go to a local bike shop (LBS) and tell them you want cheap and you want it offroad

And those Trek 820's- Good basic bikes. Gearing a bit high but I started True offroading with one in 1990. It was heavy- didn't have low enough gearing and low quality components- but it did teach me how to ride our local hills for a couple of years. Local hills- See the attachments. 30 to 40 miles on those at the weekend was enough

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Most manufacturers will make a cheap bike but try and stay with one of the Known names- Trek- Specialised- Giant are just a few. A cheap bike will not be the best for hard offroad but keep riding and you will improve. Then the bike will go up the hills and you will be thinking about the the better bike- should take about 6 months so start saving.