5km, 10km, 21.1km? Which One?
Here is a guideline for you if you are having trouble deciding which event to enter

5km
Running History- one month of running 3 times or more a week
Training Time- Four weeks of training, during which you have run at least 7kms
Once you get to 5km running all the way- and by that I mean you run out 2.5km and turn and run back 2.5km and you feel ok at the end (not dead) that means you have mastered the 5km- this takes time- could take 3 months. Then and only then do you start to grade up- and it should be only a 10% increase a week or half a km- on one run only- not all three. Two will stay at 5km and one will gradually go up to the distance you want to run.

To run a 5km event well, I think you should be up to 7km in training

10km
Running History- Two months of running 3 times a week or more
Training Time-8 weeks of regular training during which time you have run at least one 11km or 12km distance at your own pace

Once again you grade up slowly on one run a week- your other runs should be shorter and faster or a shorter run on a tougher course, so hills, stairs or off road running- this will make you a fitter, stronger runner

Half Marathon
Running History- Four-6 months of running 3 times a week or more
Training Time- Three months of regular training, during which time you complete one run of 18 to 20 kms.

21.1km is a long way to run…the half requires training, and a good mental attitude, but the thing I respect about it is, that if you do the very best you can and give it your all then you will complete it, running all the way.
I approach the half from this point of view;

If I had a 5km running base it would take a 25 week training program

If I had a 10km base a 20 week training program

Sounds like a long program, but I allow for things to go wrong, not in a negative way but a positive way. If are unwell, or suffer an injury or you need to go away for a week and not sure if you can run…its fine, you have plenty of time to play catch up in 20 weeks
I would not start a training program for a half marathon from a non running base

I think new runners should just learn to run, get to a 5km base and then stick with it for about 3 months, enter some fun runs and get used to the whole notion of running. 
Then after 3-6months (and only if you want to) start gradually increasing your distances by 10% or half a km a week (not every run) until you get to the wonderful benchmark in running, the 10km. Then enter some fun runs and work on your 10km. In the second year of running, then you could set your sights on a half marathon…if that is your goal

Your training should include
 3 or 4 runs a week, with a day off in between each run

*One long slow, steady run a week, increasing weekly or fortnightly until up to 18-20 km (you do not need to run a half marathon in training before you run your half marathon, what’s the point??)

*One 7-10km good paced run for you, so no dilly dallying on this one, find your best 10km time and always go out trying to match it or beat it, a negative split is handy as well.

*One speed session.So its fast stuff over shorter distances with recovery, these sessions are usually about 5km in distance but really hard work

*One session should be on a different course, so cross country, trail running or a hilly course or one DWR session, or if you only want to run 3 days a week, do some other form of cross training exercise, so walking, cycling, swimming, fitness class etc
Each of your sessions should be different, don’t get stuck into a rut thinking every run has to be long, that will not improve your speed or fitness or your running in general, it more than likely will make you tired and give you a higher risk of injury.

The half marathon program would probably start with a weekly km tally of 20km and build up to 40-45kms in the last few weeks