Firstly I am just a runner not an expert and secondly without knowing how fit and fat
you are this is inevitably a bit vague. I will presume you are not that fit based on your questions.
A couple of years ago I trained my 17 year old daughter (5ft 1 - 8 stones - no other exercise) from not running at all to a HM in 2hours 7 mins in 12 weeks.
We started by running on grass and she just used cheap trainers and in week 7 we invested in some proper running shoes for her (but only spent £50-£60 so low end of range). By then we were running a long run of around 7 miles on road (so probably left it a little late to get the shoes).
She never ran in anytihng more than a normal T-shirt including the HM itself.
Her first runs were 8 mins slow jog 4 mins walk 8 mins slow jog. We did this twice a week then at weekend we ran 12 mins slow jog (8+4) 4 mins walk and 9 mins slow jog and just slowly increased it every week until we got up to around 10 miles running in 10 th week with the same 4 minute walk in middle - this used to really work as a motivator in the early difficult miles.
She managed to run the whole HM without stopping.
If you can't manage 8,4,8 then make up your own combination that you can do but it needn't leave you feeling wrecked - keep it fun and 'easy' (if it starts walk 8, run 4, walk 8 then that's okay too).
Try and pick 3 mornings/nights a week and go whatever the weather - making it part of your routine will make it more likely that you keep it up.
The important thing is to gradually build it up but there is no hurry to do this - if you have someone who you can go with then even better however apart from this 12 week period with my daughter I have run on and off for 30 years and have always run alone.
Once you can run 3 miles in one go you have basically got it sorted and it is just a question of dedication and commitment after that.