PVR; I recommend Beyonwiz. Been using them for about 10 years and am very happy. The Beyonwiz forum is extremely helpful if you have any questions. No DVD watching though. There are others brands eg Fetch.
I'm sure someone will come along and tell you more about Fetch.
TV; You don't have to update as the PVR can perform most of the smart TV duties like watching content from your PC etc.
But a new smart TV will have all the catch up TV channels as well as you can watch your local movies from your PC.
For youtube I just use my phone to find content (much quicker than using the TV remote) and 'cast' it to my smart TV.
I assume you have a home network setup?
Some smart TVs can record to USB, but I am not a fan because you can only record 1 channel and the TV needs to stay on that channel.
DVD; I don't watch DVDs, but these have come down in price, so I would suggest you look around and pickup a cheap Bluray/DVD player.