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The best way to get into Middle English is just to start reading it, using a book that has glosses of difficult words on the page. If you have the Norton Anthology of British Literature, I would start with some of the lyrics and then Chaucer, as those are the easiest to handle. It may seem tough at first, but it gets easier over time. Once you feel comfortable with that, you could read Sir Orfeo which is also in there, or move to The Book of Middle English by Burrow (I think Lutefish confused this book with the one by Bennett that was finished by Gray, which is a good book, but not an anthology). The Norton Middle English Romances would also fit in here (some of these are good and some are just ok).

After doing this, you should have a good knowledge of Middle English, even by the end of a few months of reading. You could probably begin to read Piers Plowman at this point, or some of the non-East Midlands texts in Burrow.

If you want to move from here into Old English, you could. If you understand how inflected languages work (have you taken Latin?), you could get a copy of Mitchell and Robinson's Guide to OE and start working through the texts on your own. Your best bet for learning OE, though, is to take a course in it.

After you've done all that, then you could try to read Sir Gawain and the Green Knight in Middle English, maybe.

It’s a great little book, Mark Atherton is a brilliant scholar of Old English (and his work on Tolkien is equally good, if you’re a fan). It starts very easy, then works up through real texts and cultural context. The same is true of Hough & Corbett’s Beginning Old English– lots of original sections of prose and poetry, starting with basics and building enjoyment alongside the language.

If you want something that’s more academic from the start, I’d recommend Peter Baker’s Introduction, which contains a good grounding in grammar more generally, or the more linguistics-based one by the late Richard Hogg. The best overall textbook is undeniably Mitchell & Robinson’s Guide – but it is dense and (despite what the authors claim) not easy to use in independent study. Their sections on syntax are vast and comprehensive, however, so that might be what you’re looking for.

I studied Intro to Old English at uni, and we used Peter Baker's Intro to Old English:
https://www.amazon.co.uk/Introduction-Old-English-Peter-Baker/dp/047065984X

If you buy it new it also comes with online resources like worksheets which are super helpful for learning the grammar and sentence structure!

You can find the AS Chronicle here.
If you’d like to get into poetry (which is generally a bit easier to translate than prose), McGillivray has a very useful site.

I’m not sure how much of a beginner you are, but if you’re just starting out, I also highly recommend Peter Baker’s Introduction to Old English. The textbook has a free-access companion website with loads of exercises.

Teach yourself Old English is a pretty neat book, all the stuff it teaches you is from real literature. You'll also want to use a memrise course for vocabulary though.

I'm reading Baugh & Cable's A History of the English Language 6th ed. and I'm really impressed with how well written the textbook is as well as how much I've learned in the first five chapters alone!

When I took an Old English module a couple of years back we used a couple of different resources for learning the language:

• First was Wordloca (good grammar guide), which if you private message me I can send you a PDF of or you can make an account and use their website online. However, this doesn't use the long vowel markers, but if you use it in tandem with the second which was...
  
  
• Bruce Mitchell's Guide to Old English (available here) as a reader. He does use the long vowel markers you're looking for.
  
  If you're getting started with the language I would recommend starting with translating 'Cynewulf and Cyneheard' before tackling Bede's account of the poet Caedmon - both of which can be found in Mitchell's book.

i bought one myself a few years ago https://www.amazon.com/Tha-Halgan-Godspel-Englisc-Anglo-Saxon/dp/1298144256/ref=sr_1_5?ie=UTF8&qid=1475105753&sr=8-5&keywords=tha+halgan+godspel

its not a textbook but this is a great book for beginners https://www.amazon.com/Learn-English-Leofwin-Matt-Love/dp/189828167X

Bright's Old English Grammar is a classic.