Bicycle Mechanics - New Bike a "Lemon"?

Does anyone feel like helping a novice cyclist?

I bought an el cheapo mountain bike for £110 three years ago, left it in the garden to rust, and never used it. Only recently my wife acquired an equally inexpensive (pseudo) mountain bike, I took it out on the local cycle ways and loved it, so I decided to get a very basic bike just to ride for fun. I bought the bike on line for not much more than £100 from a catalogue company. I very foolishly ripped off the decals because it was a girl’s bike (I’m only five eight), so I can’t return it. After only a couple of five mile rides the rear wheel moved out of alignment and started to rub against the rear forks; long walk home; I realigned the rear wheel but it keeps slowly drifting out of alignment, what’s up with that? Also, the bike just doesn’t ride well at all, the gears keep slipping; could the bike be being slowed down because the rear brake is dragging on the misaligned wheel? My rusty bike, which is “frozen” into a middle gear and has severe rust on every major component actually rides better than the new one, I know I shouldn’t be riding it though. My wife is about to kick my ass for wasting money that could have been spent on shoes and handbags, I can only fool her that my investment only needs a few minor adjustments for so long. Help!

Rear wheel slipping out of alignment = wheel bolts or quick release not tight enough.
"The gears keep slipping" is not very clear, do you mean skipping as if the chain wanted to go to the next (higher or lower) cog? If so, certainly the out-of-alignment wheel does not help, then a simple rear der cable tension adjustment will fix that (see Park Tools web site for step-by-step instructions).

“Rear wheel slipping out of alignment = wheel bolts or quick release not tight enough”

Yeah! After I realigned the wheel the first time, the wheel did seem to be sliding to the same side, but more slowly and less dramatically, I was worried about over tightening the bolts, so cheers for that!

The only thing is that I think that the rear brake must have been set up to accommodate the misaligned wheel, is adjusting the brake feasible for an amateur?

The gear thing is either (I’m assuming) my incompetence in shifting, or something minor to do with the derailer, so I’m not too worried by that. I just think that I’ve bought a duff bike.

Thanks a lot, it must be irritating answering such basic stuff.

There are no duff bikes, just duff-ly setup bikes. Well, up to a point anyway.
Adjusting the brake varies from extremely simple to quite simple, depending on brake type. See http://www.parktool.com/repair/byregion.asp?catid=14&imageField2.x=26&imageField2.y=9 for the various prcedures. And adjusting a rear derailleur is as simple, all you need is a Philips screwdriver (maybe) and a brain (certainly).

I just think that I’ve bought a duff bike


Well, if your frame fell apart,(I've had that happen) then you might have a claim there. Most bicycle repairs are pretty easy. Get a book on bike maintenance from the public library. That should answer most of your questions. Or take it to a bike shop for a tuneup.

Your wheel slipping sounds like the rear axle has not been secured tightly enough. It may be though that you are missing a washer or something. Cheap bikes are often poorly assembled. Your gear problems sound like they are misaligned. Readjusting brakes is pretty easy. I use a bungee cord to keep the brake pads near the rim when readjusting them.

The gears slipping may be from the misaligned wheel.
I had the chain on my singlespeed start slipping and finally fall off because of a misaligned rear wheel a few weeks ago. I had just worked on the hub and didn't center the axle on each side, as a result the quick release couldn't clamp down on one side very well and the wheel became misaligned rather quickly.
Hopefully you just need to tighten your QR or bolt better.