All 3 areas have improved vastly since the 80's when they were complete dumps. Sunbury, Ashford and Staines are all perfectly fine, the trouble is, moving to any of those from Twickenham is always going to be a step (or five!) down.
Staines has a decent enough shopping centre, though not sure what that will look like post-pandemic as the anchor, Debenhams, isn't reopening.
Ashford and Sunbury don't have anything that could be reasonably called a High Street, though Ashford has a road with that name which consists mostly of charity shops and fast food takeaways. Notable exceptions are the butcher (Walton Meats), baker (Jolly Baker) and greengrocer (Ashford Fruits). For serious shopping, Kingston is only a 20 minute drive away.
Staines and Ashford are on the fast train line, so 2 and 3 stops away from Twickenham (Feltham is the stop in between) and Richmond, and you can also go out to Reading from there, though those trains are a lot slower, unless you find it absolutely right for the fast train.
Although within 10 minutes drive of Heathrow, there's virtually no plane noise, as none are in the flight path; Richmond and Hounslow get more plane noise than any of those areas. I'd say it's a bonus to be so close to the airport. Sunbury has the M3 cutting through the middle of it, which can be good or bad, depending on how much you need to use it.
Hayes is also closer than it seems, if you're going against traffic, it takes 10-15 minutes, so it's a quick journey which can be timed to miss the busy times.
Regarding house prices, Staines is the most expensive of the 3, with Ashford and Sunbury on a par, depending on which part you are in. I'd worry about flooding with Staines, as lots of it is close to water, same with Sunbury (which is also an "on-Thames"). Ashford old town (around the train station) has some lovely Victorian and Edwardian houses, though likely to be out of budget. The cheaper houses away from there are not as nice, and can be a bit hit and miss.
If I were you OP, I'd travel down to each of those areas to get a feel for which is most homely to you, drive down some side streets and perhaps view a few houses.