|WHAT?! Chamonix is incredible, if it's your first trip to the Alps you should totally base yourself there. I went there for all of June last year in what was planned to be a once-off trips to the Alps... now I'm intending to spend every June there. There's so much to do, especially in the moderate range you describe. If conditions aren't on for the Mont Blanc range there's heaps of more moderate stuff in the Aiguille Rouge range. And it's just an hour through the tunnel to Courmayeur in Italy, which opens up a whole new area (and great coffee, which is the one thing Cham lacks).
A great guidebook is Laroche & Lelong’s ‘Mont Blanc Range - Classic snow, ice & mixed climbs’; others include Batoux’s ‘Mont Blanc – the finest routes’ (more of a coffee table book than a guidebook), and Moran’s ‘4000m Peaks of the Alps’. There's also heaps of excellent guidebooks available once you're there that I couldn't find in Aus or for purchase online.
Finally, it's possible to spend time in Cham without breaking the bank - get an apartment through Airbnb, don't eat out too much, go for foot access rather than the lifts if time and conditions for your objective allow, etc.
Happy to expand on any of the above, PM me if interested.