Definitely take those days off in between! It's not really your muscles that have a hard time adjusting at first, it's your bones and tendons. Those need time to heal and adjust to the impact.
Shin splints suck. Make sure you're warming up and cooling down enough. The more walking you can do before and after your run, the better. I like to stretch after I run because my muscles are warmed up, but be careful not to overstretch. It shouldn't hurt at all. Lots of shin problems can happen when your calves get too tight or overdeveloped. Make sure to stretch out those calves, or roll a rolling pin over them (carefully) to get out the knots. Toe taps help strengthen your shins too. They are amazing for preventing shin splints. Also, for sore muscles or knees I like to use ice massage. Take a paper cup and freeze some water in it, then peel off the bottom and use that to massage whatever hurts for about 5 minutes.
One more thing. The hardest thing for me when I was towards the end of the program and a beginning runner was to slow down on my runs. It sounds counter-intuitive, but slowing down gives your body a chance to adjust to running, and can help you build up distance without injury. Also, your lungs will give out long before your legs do. Even now my long runs are always slow. It's hard to judge when you're first starting because I remember being out of breath all the time, but it gets easier and eventually you'll get faster without trying.
Re: motivation, it makes it a lot easier to get out there if you have an actual 5k to train for. Preferably one you can tell everyone about so you can't chicken out at the last minute
Sorry, that was probably too much information, but I just get excited reading this thread. Can't wait to see you all graduate!