I have a Galaxy S4 and I cracked the screen. So far the phone is working normally. The cracking is extensive (lots of small cracks), but my screen protector is holding everything in place and the phone is working normally. I expect this will hold up for too long. The phone is out of warranty and I don't have extra insurance from Verizon.
Can anyone recommend a reputable repair service?
I personally would look locally. You can search on Yelp.com or just do a Google search. Some things you want to ask when they give you a price is if that includes everything; the new screen, tax & fees etc. Usually you can get a screen replaced for around $100.
If you're technical savvy you could also just buy the screen online and replace it yourself.