If you're confident that you're jobs are secure and are committed to the area long term (big IF), buy something for $2–2.5 in a great neighborhood and be done with it. You might be able to stretch closer to 3. Focus on schools and location – you can always add on or remodel later. Barron Park or West Menlo Park could be feasible.
We're not physicians but went through a similar amount of training. We were fortunate to pick up a couple of properties on the Peninsula during the run up from 2010–2015. Our salaries were much lower than they are now but so were prices and we made it happen. Both are in very central locations with above average but not excellent schools. With three young kids we're now looking for a long term place in the $2.5–3 price range you've described. I'd like to do it without selling our other properties but that may be more of an emotional than a rational decision given how much they've appreciated. Having followed the market pretty closely for the last 8 years my gut tells me it's finally starting to plateau. I've felt this way in the past and have so far been proven wrong.
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