GoToWebinar all the way. It's a bit pricey (but not too much), but it's by far the best solution out there.
The last thing you want to do is use a free/cheap but unreliable provider and have your webinar experience massive connectivity issues or drop half way through.
you can start off by using Google Hangouts, which is free and not too difficult to set up: http://www.smartpassiveincome.com/hangouts-on-air-for-webinars/
And once you're ready to go, I'd suggest GoToWebinar - they're one of the most popular webinar tools out there.
It totally depends on what you care about the most. I've used pretty much every platform out there–if peace of mind is your top concern, go with ReadyTalk. They take the stress away with excellent customer service and a dedicated rep to sit in on your call. But if you want engagement metrics (who clicks away) and cleaner sound, GoToWebinar might be better. Their UI and customer service leave something to be desired. For a roundtable where you don't need in-depth tracking, use Google Hangouts. I'd be happy to talk more about all the options out there.
My choice webinar platform is EasyWebinar (http://EasyWebinar.com) because they can do both live and automated webinars. You can either pre-record your webinars and play back the video as if it were live or you can use Google Hangouts and then with a flip of a switch turn that hangout into an automated webinar replay.
I know a lot of people love GoToWebinar, but I prefer methods where the client doesn't have to download anything to their computer. That makes it feel like a bit of a dog to our people.
Depending on your budget and needs, here are some that we've used and liked:
Pros - Low-cost entry, can embed the code on to your own page, public chat room available, very reliable (I've been using it for five years and have never had any failure or technical issue and we've had up to 3,000 participants on this one.)
Cons: Cannot download the replay in video format, but can replay it and embed. Also, this is a powerpoint only type webinar (no screen share or "you on camera")
Pros - low-cost entry point, chat, pop-up boxes, can brand with your info, analytics on exactly who watched your replay, versatile - you on camera, powerpoint, play videos, share your screen, do it all. Stable with crowds (we've had up to 3,000 on this one too.)
Cons - no embedding, a little buggy on the audio (guests sometimes have to use the phone in option.)
Pros - One-time investment instead of monthly, nice "wrapper" for Google Hangouts, dynamic - lots of functions and lots of ways to share info.
Cons - Higher learning curve, higher one-time investment
Pros - Easy to use (registration page, view page are one), Nice templates to choose from, reliable and sound (no tech issues ever), dynamic (too many options to list including a built in affiliate program.)
Cons - Facebook only (but if this is where you are meeting with your audience or if you are selling a social media product, then this is THE tool.)
There are so many more out there, but I just wanted to share those I have personally used often.
Best of luck with your research and your project!