This is something that was brought up on my QL2 a few years back and shaving was something everyone dreaded to do...especially when you have maybe 20 minutes in the morning to sh**, shave, get dressed, get downstairs (no time to shower) in a couple of sinks with 6 or 7 other guys who have to do it at the same time as you. So, the instructors put it up the chain and got a doctor to talk to us on the weekend. He said two things and they worked for everyone very well and has been for years especially when you are shaving every day like clockwork (unless deployed on NBCD or LRP when you look like a bag of hammers anyways):
1) DO NOT shave against (upwards) your beard grains as it disrupt your facial pores and can cause chronic razor burn (and it looks worse than just "redness" after shaving and can cause infection). The best thing to do is use warm NOT hot water as hot water dries your skin excessively (especially in the winter) and the razor tends to take off small chunks of your face in the process, leaving you looking like a someone coming down with chicken pox. Also when shaving, shave sideways (except for the neck which should be shaved in a downwards motion) and neither up or down because shaving down does not always clear the grains and shaving up causes damage.
2) After shaving, the best aftershave moisturiser to use is Nivea as it is fairly mild and you don't go running out, screaming like a headless chicken.
3) If you are new to shaving everyday, don't head over to the MIR at the first sight of razorburn. It is natural for your face to get adjusted to the shaving regimen between 7-10 days and yes the daily KILL BILL bleeding does stop. Just remember to not keep using the same old razor for weeks on end and you don't have to go out and buy a Mach 4 Champion or a Shick Quattro 4 (as the excessive number of blades are NOT suited to all skin types and a really close shave everyday is NOT for your skin good everyday, especially when you shave daily), leave the cylinders to cars and the Speed Channel. The best razor to have is a twin blade and the Gillette senor and sensor excel does the trick very well and their blades remain sharp for up to two weeks (for me anyways).
PS: You won't get in sh** for razorburn on training but you WILL get it if you don't shave and if I still remember correctly it will cost you a $50.00 charge each time they catch you unshaven w/out a chit which gets max'd at time 3 and after that you are put before the man and well...
Hope that helps!
Cheers