Just a heads up; when you get to OCS and do the indoc PFT those 20 pullups will probably be around 15. Your 79 crunches will be around 60. Your run time probably won't change. The Sgt. Instructors are notorious for being sticklers on pull up form. If you don't do it exactly right they will just repeat the same number for every pull up until you do (i.e. six....six.....six....six....). So make sure you are not cheating yourself by not doing the correct form. If you do poorly on the indoc PFT you will be put into remedial PT and not allowed to leave base for liberty (after the first 3 weeks). I knew a guy who didn't do well (I don't remember the minimum) but he didn't leave base until the week we graduated!
If you do pull ups palms forward make sure you extend all the way down until your arms lock out, then pull back up. If you do them palms out it is easier to lock out your arms, especially if you use a wider grip. Doing pull ups palms out is harder at first (if you've never done them that way before) but once you build up those muscles you will pump out 20 good pull ups no problem. A good training technique is to do pyramids. Start by doing one pull up -- then ten push ups, then two pullups -- ten push ups, three pullups --ten pushups (you get the idea), then go back down. Say you get to 7 pull ups -- ten push ups, go back to six, then five, then four, all the way to one. This works wonders. I think the good gouge is if you can get up to about 12 with pyramids, 20 pull ups will be no problem. Good luck!