Mongoose is also a "dept store" brand.

The fact is if you want to spend $50ish, then dept store bikes are your only option for new bikes.

If you're willing to buy used, you're better off because the LOWEST quality bike you can get will be the same as the dept store bike you're looking at. So without knowing much about bikes, you can buy a used one and be fairly confident you're not going to get a particularly BAD deal.

Now, that being said, test-ride the used bike first obviously. As long as it is reasonably comfortable and the brakes and shifters work, it'll be as good (and probably better) as the $50 bike you're looking at in target.

To answer your question #3 which I don't think anyone else commented on much, mountain bikes are more popular to the general not-very-bike-knowledgeable public, so most lower-priced bikes are mountain bikes. You can spend a couple thousand bucks on a mountain bike just like on a road bike, but the lower-end on mountain bikes goes lower than the lower end on road bikes.

In the used market however the playing field is completely level. People buy $50, $500, and $1500 bikes, ride 'em for 5 minutes, stick 'em in the garage, then 10 years later sell 'em at a garage sale for $25. So you can find great deals and you can find not-great deals, but you're very UNlikely to find a ripoff. A bike store (as in, "Bob's Bikes" or whatever) will usually do a "tuneup" for in the vicinity of $40-50 (if you didn't buy it there. If you bought it there, often tuneups are free), where they'll lube everything, make sure your brakes and shifters are adjusted, sometimes even true the wheels. If you get a used bike for $25 then your total cost is like $75 and you'll have a pretty good bike. This may be worthwhile even if you get a new low-priced bike just because the guy at target who assembled it may or may not have known what he was doing.