I always end up on these threads as I have direct experience of all your short listed places. I was brought up in Dunblane, married DH who is from bridge of Allan, have lived in dollar for fifteen years, in laws live in auchterarder and sister lives in Linlithgow.
by the way, Kingaelfred Dollar I'd definitely NOT drier that BofA!
Dollar is the most villages of your choices, really good for preschoolers and primary age kids, a bit rubbish for teens as secondary school choices are not straightforward. You would not be unusual being English.
Alloa is cheap for a reason, it is much more working class than your other choices! harder to fit in as a non-local.
Dunblane is the sensible choice, good for all ages, teens and little ones, good community spirit, quite expensive, good transport links.
Auchterarder has some nice bits and a good school and high street but is worse for transport, gets more snow in the winter, when the A9 can be dodgy.
BofA, is very pleasant and has a nice primary school, residents can be a bit more " materialistic" than in your other choices ( in- laws sold two houses to footballers!). The catchment high school is not as well regarded though.
Large character properties are at a premium in all these places and you would struggle on your budget, seventies and eighties houses on estates could be found in all places for around your budget as long as you are not too fussy about architecture!
basically, if you see a lovely Victorian villa with four bedrooms in Central Scotland on your budget it will be in a rougher town or a remoter area.
Scotland is generally better at small towns than villages, many of the villages near Stirling are ex mining or mill villages.
Have you tried Gargunnock or Doune?