Be brave - go into the bike shop, admit you know nothing, what can they recommend? If they're any good, they will be helpful (so maybe try to avoid Halfords, I have never had a good experience with Halfords, whether for bikes or car stuff or anything).
A trailgator won't work with stabilisers - as PandaG said, you can get flip-up ones, or you can do as my friends have done and fit quick release ones instead (although I must admit I'm not sure WHY they've done this, and not gone for the flip-up ones).
If you want to sound like you have a clue in the shop, you might want to suggest a hybrid bike - hybrids have straight handlebars like a mountain bike, but narrower, slicker tyres (not as narrow or slick as racers/road bikes though). Mountain bike tyres cause LOADS of friction, so are hard work, hybrids are easier ot ride. An aluminium frame (rather than steel) is a good idea too - let's just say, the first bike I bought as an adult was a steel mountain bike which felt comfortable in the shop but turned out to be too small; I road it about ten times. I then spent over twice as much money on a Trek hybrid which had more use than that in the first month I owned it. I still don't ride it enough, but DH rides Treks to death, keeps buying them!
Some manufacturers do bikes which are not only women's bikes as in they have a dropped crossbar, but are even more tailored to female physiques (Trek's is called WSD), mine isn't such a thing, but as you're small it might be worth checking out, they have narrower handlebars, shorter distances between handlebars and saddle, etc.