Actually, I haven't re-read the first series in many years so I can't be totally sure. But if memory serves, after issue #11, TMNT Vol. I had very little continuity outside of a few two or three-part story-lines up to #45 (the first of which is "Return to NY" issues #19-21 - which are included in The Works Vol. 3).
I personally don't think you'll miss them in terms of continuity and you can always get the originals from eBay, online shops, or local comic shops for pretty cheap.
And, quick correction to my previous...I just checked The Ultimate Collections from IDW and, while I thought IDW had gotten permission to reprint #13, 16, & 18...they apparently did not. The Ultimate Collection Vol. 3 also does not contain these 3 issues. My bad.
I'll add to this and say that the issues included in The Works are the ones that Eastman or Laird directly helmed. #13 Was all Michael Dooney (writing and art) and featured the characters Complete Carnage and Radical. I'd recommend getting their backstory from Tales of the Teenage Mutant Ninja Turtles. The issue is a one-off and won't affect the Eastman/Laird continuity in the slightest.
#16 is the start of Mark Martin's 3-part story that ends in issues 22 and 23. The story is a bit abstract and also doesn't relate to the overall story.
#18 is a bit different in that Eastman did work on it with friend Mark Bode. They collaborated again on issue #32. Again, this won't affect the story.
The main story you're looking for is contained in the issues Rich mentioned. If you've seen the first live action movie, you'll see that major plot elements are borrowed from the comics though many are heavily altered. Basically, the end of Return to New York (issues 19-21) would coincide with the end of the movie. Eastman and Laird wouldn't collaborate and put out a chronological "canon" story until issue 50 with a 13-part story arc called City at War to finish volume 1.
Eastman and Laird were so busy with everything else (toys, the show, etc.) at the time that they left the comic up to one-off artists and writers. That's why volume 1 is so disjointed and diverse.
The Ultimate Collection hardcovers do a nice job of getting the core story reprinted. If you want the extras, check out the TMNT "Classics Collection" of TPB's with great covers by Michael Dooney. Those collect the missing stories and I don't think any issues overlap.
Thanks for all the info guys.