The RJ11 jack in the back of your PC - if it really is RJ11 and not the typical RJ45 used for Ethernet (LAN) - is part of an old analogue modem. It isn't for connecting a telephone handset, it is in a way a telephone itself. It is to be connected to a landline just like a landline phone, it is NOT to be used with a telephone connected to it.
The purpose of the old analogue modems was to use use dial-up internet services and some also had fax capabilities. Some models also had a second RJ11 connector for a telephone passtrough the same way many fax machines allow the same functionality. But it's fundamental to understand is all this devices work connected to a landline in your house/office.
Hard to believe there are still computers with such devices in 2018 but perhaps in some rural areas in the USA there might be people still using them with a legacy dial-up service. Other than that they're pretty much useless and even with said dial-up service the best you can do nowadays is to download/send small text only emails with an email client software. Just opening the GMail webpage, for example, can take more than 10 minutes (just a guess, it may be even worse).
Having a phone number via internet is quite common and can be provided by Google Voice, Skype or hundreds of other providers worldwide. The requirements are just a device (PC, tablet, etc.) capable of running the software and a broadband internet service. It has nothing to do with handsets connected to the PC though. Most people use the same audio devices the PC already has, typically with headphones/headsets. Again, the RJ11 connector can't be used with this kind of services. The device where the RJ11 connector is attached to is and has been obsolete for the most part of the last 20 years.