Get yourself a smart TV, they're great!
You may find that your Virgin package won't work with a 2nd TV though. We have Sky, and although the 2nd smart TV works wonderfully as a 'stand alone', to use it with the full Sky package, films, sport etc we have had to increase our subscription to Sky Q (for any Sky users amongst us, Q is brilliant by the way!).
We tend not to use the TVs to surf the net, as typing using a remote control isn't the easiest thing!
The first smart TVs were okay, but didn't have many built in apps, and not many were full HD (high definition). However, with the apps built in to the newer TVs, there are loads of entertainment opportunities.
If your Virgin package includes HD, make sure you get a TV with Full HD, and if possible UHD 4K. The clarity and definition is fantastic.
Also, get a TV with at least 3 or 4 HDMI ports for connecting BluRay players etc.
Our TVs are both Samsung, can highly recommend the brand.
Get your DD to go with you to a big retailer, so that you don't get 'blinded by science' and have a look at them.
Check with Virgin first though if you want to use their package with a 2nd TV, it may be possible, but could also increase your payments quite a bit. You may want to give that some thought.
Good Luck!