Old English

Hwæt!!* I only have an undergrad module's worth of OE knowledge, but I dug up some old reading lists. A lot of these are academic texts so they tend to be a bit on the pricey side, I'd recommend trying to pick them up secondhand where you can.

The main book I was recommended was Bruce Mitchell and Fred C. Robinson, A Guide to Old English, 8th edn (Oxford: Wiley-Blackwell, 2011). A quick search-around hasn't revealed any later editions, so this is prooobably still the most up-to-date one.

Some other guides:

Mark Atherton, Complete Old English: Teach Yourself (London: Hachette, 2012)
Peter Baker, Introduction to Old English, 3rd ed. (Chichester: Wiley-Blackwell, 2012)
Richard Marsden, The Cambridge Old English Reader 2nd ed. (Cambridge: Cambridge U.P., 2015)

Texts in OE:

Elaine Treharne, ed. Old and Middle English c.890-c.1400: An Anthology, 3rd edn (Oxford: Blackwell 2010) - one of those lovely chonky, comprehensive anthologies. I used this one so much back in the day. It's got facing page translations, which are super useful.
Dumbarton Oaks Medieval Library (Cambridge, MA: Harvard U.P.) - lots of different volumes of Anglo-Saxon poetry with facing-page translations.
Robert Hamer, A Choice of Anglo-Saxon Verse, (London: Faber 2006)

Texts in Translation (but it's all Beowulf because that's the only one I've read enough translations of to have opinions about them):

Roy Liuzza's translation is the one on my reading lists, and (I think?) considered the best from an academic perspective.
I remember enjoying Seamus Heaney's well enough - he very much approaches it as a poet, and it's pretty striking as a result.
Maria Dahvana Headley's is honestly inspired. It doesn't aim for a "pure", word-for-word translation, instead seeking to capture the vibe of the poem and transmit it to a modern audience. It rules. I love it. Translating 'hwæt'* as 'yo' is actually genius.

Context and Background

John Blair, The Anglo-Saxon Age: A Very Short Introduction (Oxford: OUP, 2000).
James Campbell, Eric John, and Patrick Wormald, eds. The Anglo-Saxons
(Harmondsworth: Penguin, 1991)
Hugh Magennis, The Cambridge Introduction to Anglo-Saxon Literature (Cambridge:
Cambridge University Press, 2011) - Cambridge Introductions my beloveds, they are so so useful for getting a quick grounding in a literary period.

I hope this is useful! There's probably some more recent resources I'm not aware of, but these are what I used. This also looks like a pretty great resource.

* For those not in the know: hwæt = something in the realm of 'hey, listen up, I'm about to start talking'. Older/more traditional translations have gone for 'hear me' or 'indeed', Heaney (controversially) uses 'so'. (I once had a lecturer shout "HWÆT!" at everybody to get them to stop talking, 10/10 experience.)