Hi there! I have a marketing consulting business and help B2B companies do this a lot.
There are a few webinar platforms out there.
Are you expecting hundreds of people to join? Do you want to record the webinar and post to your website for future use?
The main ones are:
Gotowebinar (these guys have been around forever)
Zoom (these guys came out of nowhere and are doing really well)
On24 (pretty nice solution, might be more than what you need but also a very good platform)
You can either integrate a web registration form to your website or simply post a link from your site to their registration page.
A lot of this depends upon your needs and budget. What you might need/afford is something more basic like a web conferencing solution, think Skype for Business.
Let me know if I can help you pick a solution. I don't do the website integration stuff but that's pretty easy for a web developer if you've already selected the software. All of those solutions will have well documented developer instructions for adding the registration form to your website.