I would avoid Safelite, but you should be fine with any other major glass shop/chain. I wouldn't expect most dealerships to have the tools and/or expertise to deal with windshield work. Cutting tools around paint/cabin plus really unforgiving adhesive make for some risky work best left to those who do it every day.
Insurance typically covers it, but you'll want to just compare the cost with your deductible. Good shop front office employees will basically do this for you before you're even giving them any money.
That said, replacing a windshield only for rock chips is usually not as cost effective. Chips can be filled to an extent to keep them from spidering out (usually like a $50/chip procedure), but you could replace your windshield and tomorrow get a new chip and be sad. Unless your chips are large and/or impeding your vision, it's usually best to just live with them. That's just my thoughts, though.
Chips don't usually affect the integrity of the windshield, but cracks do.
(It was many years ago, but I've done a summer stint at a windshield repair/replacement [Harmon] shop in my past.)