Has your uni library a copy of the 2013 second edition of An Introduction to Gödel’s Theorem? Do please check! It’s a lot better in lots of ways than the first edition (indeed, ideally, the first edition could be quietly put into the library store), it’s still relatively cheap, and it’s very definitely what your students should be reading instead of the first version. Then I won’t find myself cringing thinking about people reading the dumber bits of the first edition! Anyway, if it isn’t already on the shelves, now is the time to order the lovely new second edition to be available in time for next academic year. (This recommendation is of course not motivated by any concern to spread the truth but by the hope of massive financial gain …)
The Teach Yourself Logic reading guide to logic textbooks, aimed at beginning grad students or thereabouts, is now at version 10.1, 136 exciting pages, and a real snip at zero pounds, zero dollars, and zero anything else. The current version (and yes, I know it’s time for another update) can be downloaded via the stable URL https://logicmatters.net/tyl/ — students do keep saying that they find it pretty helpful, so why not check that it is mentioned in the relevant logic course handouts?
The LaTeX (not just) for Logicians site has been going for about 10 years — gulp! — and covers everything you’d expect plus some. It seems more relevant to more grad students than ever, given the popularity of using LaTeX (or close variants). I still tinker with it when I stumble across worthwhile additions (and please do let me know about anything I should add). This too has a stable URL, http://www.latexforlogicians.net which really ought to feature in the relevant info pack or on-line resource webpages for graduate students. Again, worth checking whether it is appropriately linked?