This is almost impossible to answer without a little more about your interests and preferences but maybe try this :
http://www.bbc.co.uk/radio4/arts/ago...ogrammes.shtml
It's from a BBC Radio 4 show called A Good Read where three people each suggest a book that the others read and discuss. They don't always agree. (If in the UK you can listen to the programme on catch-up.)
It includes a wide range of topics and styles - mostly fiction I would say but not always. The list has the benefits that a) it's not limited to either just modern or classical work; b) you might get an idea of the book from the person (if you recognise the name of course!); c) no one genre predominates.
Personally I would say just now make sure you have read George Orwells's 1984 as it stays absolutely pertinent in these days of Trump and the danger of totalitarianism. Also Catch-22 cos its funny and wise and the construction is so amazing. And His Dark Materials by Phillip Pullman is fabulous, a page-turner and totally engrossing. But there are several hundred more I could mention...