Third Party | Self-Build
For convenience, the suggestions already on the table are the best option. WebEx is of course an industry standard in the business world.
Other options, of course, could be combining two or more third party options. You can separately utilize voice and drawing applications, voice having many different kinds. Drawing options are available in Java, but I haven't taken the time to look into commercial availability. WebEx is great in that you can share screens and do remote takeovers.
While having someone develop you a program is less convenient and less cost-effective, it does offer the benefit of being potentially more private, more custom, and if you have a good developer they can show you how and why it works. If you have a really good developer they will also guarantee it. In any case, by using a developer you'll know that tech support knows what they are doing because it's the same damn guy that wrote the thing, but he's probably charging you for that second call.
Is this for business or personal? Personal, go with something or many somethings that are free-ish. For business, definitely recommend hiring a developer because your clients will be impressed by custom work and you'll be happier with a product that does everything you want.