Thanks for posting the link. Of course, that is just a list of your favourites. It doesn't show what classics you have read but didn't get on with. I think you might consider exploring various aspects of the classics that were missed out in your degree, and of course, looking beyond literature to such things as philosophy and history.
If you don't know them well, you might be interested in exploring some of the great Ancient Greek dramatists. You don't say you know the language, so that would have to be in translation. I suppose starting with a couple of background books, one on the Greek myths and one on Greek drama would be helpful before exploring the plays themselves. If you can get to see theatre productions that is the best way of becoming acquainted with them. The next best thing may be audio versions. I have found that that is a very good way of exploring things like the
Iliad and the
Odyssey as well. The fascinating thing about the classical Greek drama is that it can be so immediate and speak to us today, even after two-and-a-half thousand years and yet at the same time embody beliefs and practices that are totally alien. The basic idea of tragedy stems from this source.
Obviously, if you didn't do Old English, you won't be able to read
Beowulf, but you could enjoy a good translation, such as that by Seamus Heaney. Since you can read Shakespeare, you could slip back slightly further in time by reading Spenser and Malory. Malory is great fun, and you don't have to be an English specialist to cope. My son, whose degree was in engineering and computer science, managed to read
Le Morte d'Arthur with no trouble at all. You can also get an excellent recording of it if you prefer to listen. I love Chaucer, but there is no doubt that his language makes him a bit harder to read. You really do need glossaries to understand every word. Depending on whether you can cope with Chaucer or not you might try other Middle English texts like
Sir Gawain and the Green Knight or
Piers Plowman. The former in particular is much harder than Chaucer because of the dialect.
You might also consider reading some of Shakespeare's contemporaries among the dramatists, in particular Marlowe and Jonson. Of course, as with Shakespeare, it helps enormously to be able to see theatre productions of the plays. I don't know what sort of access you might have to classical theatre. I have been fortunate over the years in being able to see Royal Shakespeare Company and National Theatre productions of almost all of Shakespeare's plays and several of Marlowe's, Jonson's, and Tourneur, Webster and Beaumont and Fletcher. the Shakespearian period was very rich in excellent dramatists. The more one reads, the easier it becomes to read more.
Please let me know what you think of my suggestions. If they are helpful, I'll continue with another few years' worth of reading.