If your computer meets the requirements for Windows 10 (which it should, the hardware requirements haven't changed - the only issue could potentially be a legacy hardware device that doesn't run on Windows 10), then installing Windows 10 on your current computer is fine. You can do an in-place upgrade, meaning your files and programs will be transfered over to Windows 10 - you won't need to reinstall everything. Generally, the in-place upgrade works smoothly, but if there are any issues you're at the right website to get them fixed
There is no imminent "your computer will explode on the 14th Jan" threat, but we cannot predict the future. It might be years before a serious Windows 7 flaw is found and attacked, or it could be days. No anti-malware solution is perfect, and they can't fix vulnerabilities in the operating system.
Windows 10 has been out for 4 1/2 years now, and whilst there were definitely issues at the start, it's now a very mature and stable OS and I can't think of any reason I'd want to stay on Windows 7. Yes, I liked Windows 7 a lot - as did many people. There are some things in Windows 7 I miss, don't get me wrong, but Windows 10 is a much more secure, faster and more modern OS and there's very little reason not to upgrade.
Paying for extended support does not really make sense unless you are a business that must stay on Windows 7 due to a specific business application that refuses to run on Windows 10 and where virtual environment is not an option.
Extended support for Windows 7 is only available to businesses and enterprise organisations, and only for Windows 7 Professional/Enterprise devices. They're only available through a Microsoft account manager or authorised partner.