10% - 15% upon job start should be okay to start, make sure they have the permits in place. They too don't know you and so they want to be sure they will get paid too, which is why they ask for so much upfront.
If you are concerned of them walking away, you can ask for an insurance on the project. It costs money but it will protect you in the case they walk away or abandon the project. Don't forget that they should pay if they a mistake on the countertop, they should pay for emergency shipping or give you a reasonable estimate on the time it will take. I have heard the excuse of "there is a backlog on parts" happened to a neighbor of mine and delayed the project an extra two weeks. I just went through a basement reno which got extended from 4 weeks to 6 weeks. Did the punch list just two days ago.
A 10% - 15% retainage should be held to the end upon final completion after punchlist is completed.
Make sure you talk to your contractor and make sure he has the funds to perform the job, this could be why they are asking so much in the front end. Make sure the COI insurance has you listed as an additional insured as well.
You can always ask for a modified payment schedule if you are really uncomfortable. They should be agreeable.
10% Upon start
25%
25%
25%
15% final acceptance
good luck.