all of the neighborhodds listed are good places for raising a family, Chatham would be considered on the southeast side however.
Property taxes on the southwest side have gone through the roof, mine are up 46%, some neighborhoods like Englewood are up as much as 74%.
Not much new construction going on in Ashburn or Beverly. I am unsure about Chatham though.
The biggest payoff
The Chatham area has been all the brink of becoming a top south side neighborhood for 20 years due to its proximity to Jackson Park, the lakefront and Metra Electric Line Train Service. It has been held down due to its proximity to poorer neighborhoods, but now that the south loop has become a world class neighborhood, other areas such as Bronzeville, South Shore, Oakland and Chatham are being bought up in droves by real estate speculators.
The safest bet
Ashburn is a bedroom community with very reasonable housing prices on standard size lots. Lots of block parties and neighbors looking after neighbors around here. Expect about a dozen people with home made apple pies at your door when you move in.
The most to offer
Beverly has been working on beautification of some of the nations most glorious homes since the early 70's, it features the 2nd largest historic district in the nation where the top architects of the turn of the century built everything from villas and castles to cottages and bungalows. The lots are exceptionally large as well, a 25x125 lot would be considered small in an area where 50 x 300 lots are not uncommon. The area also features the best schools on the south side and a very organized neighborhood association.
www.bapa.org
My advice would be to come out and check out the areas before making a final decision.