Go to the SBB website and have a look which train connections there are? Also check the bus connections. And then you can see what areas are available.
Ittigen is probably the cheapest area of all the " suburbs" around Bern. I wouldn't say it's any worse than the other ones, so if you're already working there and your budget is quite low, I would look there.
OP, city centre will be too pricey - Ittigen is quite nice.
Bumpliz is more affordable, but many avoid it due to some rather depressing cold war era high rises. Almost anywhere in the Bern area is a nice place to live.
He mentioned having a family. Call me a snob but my parents in law live near the school in Bumpliz. I wouldn't want my kids going there if I had a choice.
Maybe a bit late but we moved to Ittigen as a family and we are happy here.
Also agree with the poster above, we considered Bumpliz as it's also affordable with good connections however it was a bit too multicultural for our liking.
Always appreciate when a poster adds a followup so thanks for that.
I do want to specify that my issue with Bümpliz wasn't one of multiculturalism (we're almost all foreigners here one way or another) but rather due more to economic issues, the kids there seem to be less supervised and less well-behaved then the children from other neigbourhoods.