BiBalles I agree re Littleover - it's quite sprawling in the middle and there is a lack of direct route buses there so you do need a car. But OP can afford to buy around the little HIgh St - there's now finally a good coffee shop there attached to the Co-op. And good buses, walkable to the centre too in about 25min.
Alvaston around Sharrow Rd does have an advantage of a very good quick airport bus.
Tomnook I agree with BiBabbles that you can't just accuse someone agressively in 'talking rubbish'. You can state your opinion but that's what it is - YOUR opinon. OP being my age and from London, and I had also moved as a single woman, is likely to see things similar to my view.
First of all I was not advising OP to go Chaddesden as a first choice - I clearly said I much prefer Darley park area to anywhre else. I said Chaddesden is a nice enough suburb and is located on the way towards Nottingham. And that's exactly what it is. I don't think OP is planning to walk around the streets at night frrequently on her own - this can be risky anywhere. In the daytime is perfectly safe, and so it at night in the nice streets where she would go, she's not planning to buy a cheap house on estate.
There are also a few good small chain supermarkets there which other suburbs lack. Alvaston I'm not a fan of myself, but some bits are nice enough and it's close to Elvaston - I advised that because she might want to look, having an interest in walks / parks.
The other thing is, OP clearly said she is coming from a not very nice area of London! So her perspective would be very different from someone who lived in a town all their life and is too sensitive to any rough around the edges bit of an otherwise good area. London is mixed everywhere, and to someone from 'not a very nice' area, all these subrubs would feel quiet and safe. I actually lived in a posh area of London before moving here, and I don't see these areas as unsafe or unpleasant - they ar very clean as opposed to London, people take pride in their gardens, park their nice cars on the drive without fear of damage, etc. I don't like some areas of Derby, same as in most places (Normanton or Cavendish - or the boring and somewhat insular Mackworth).
The middle part of Chaddesden is perfectly pleasant and many nice people (families too btw) live there - I don't know when and why did you spent time there but I was looking recently at many houses, and all the owners were nice, decent people who lived there for many years. All LOCAL apart from one young couple who used to be in Notiingham (since being local is everything to you). They were moving to a larger house or for work, all felt like happy homes / people. So I'm sorry but I can say exactly the same - that they would all say you wre talking nonsense. Yes, one side towards Breadsall is an estate end, and also up Washington Ave, but all around the park and all te streets around Max Rd are nice.