Busted Dept store Mongoose Shifter - Scrap or Fix My wife convinced me that we should buy bikes (2x$100.00) @ a dept store. I found a Mongoose (which I can remember used to be decent) and within 6mos I broke the bracket that holds the shifter in place (not sure on my lingo here).  It says it is Shimano, but I don't know if I would be better off trying to replace it on my own(I am a smart DIY guy but have no experience w/Bikes), taking it to a bike shop, or just looking for a used Trek hybrid on CL?
Please advise.
If it is easy to get the bike to a bike shop, it is worth asking the shop the cost of a replacement.  It is not likely to be more than a few dollars.  Otherwise take the old bracket to the bike shop to get the replacement to match.

If the bike shop is able to do the replacement on the spot, let them do it and watch how it is done, otherwise it is not hard to do yourself and will save you the time of having to collect the bike.

This you will be left with a cheap bike that you can ride.   You may still wish to buy a better bike, but will have the time to find a good one.