Which visa to apply for visiting USA when working with/providing a service to a USA company?

No, an H1b is not the appropriate visa for your situation.
An H1b is a work-visa and it is sponsored by & applied for by the company in the USA in order for you to become a full-time employee of theirs - living & working in the USA.
There are limited numbers of these visas issued and applications are generally only accepted at a specific time of year.

What you need is a B1/B2.
I was in much the same situation as you are in (although it was 15 years ago) - owned my own consulting business and wanted to 'visit' a customer in the USA with which I'd had an ongoing business relationship for the previous year or 2.
You'll need to show convincing evidence of a legitimate ongoing business in your home country to which you will return and you'll need to show that your business will survive with you being absent for this period of time.

I had been running my business for about 3.5 years at the time I applied and could show tax returns and other evidence of a genuine operational business.
I had documentation from the company I was to be visiting stating the purpose of the visit and that they would be covering all of my costs.
I was only issued a single-entry visa, valid for less than 2 weeks, on that occasion, but subsequent visas were issued for 6 months and most recently for 10 years (since I behaved myself and complied with all of the rules).