As long as you have good shoes that are not getting past their life, the biggest bang for your buck for a beginner is overall volume. More is better when it comes to running, but you need to do it in a small increment fashion.
The first consideration is how many times a week you are running. Since you are running 3x week currently, at ~ 2.5k (1.5 miles for our imperial audience) per run, I would suggest that you don't increase the overall volume (7.5k for a week) but that you run more days for less per day. I would run 2 days at 1 to 1.5k each, take a couple days off. Run a day of 1k, then a day of 3 - 3.5k, then a couple days off. Lather, rinse, repeat for a few weeks (2-4).
Once you have that down, keep the distances the same, but add another day of 1-1.5k instead of one of the days of a two day rest (I would suggest that you not do it after your longest run to start). Do that for another couple of weeks. Self monitor, but keep adding days on that type of progression, until you are running at least 5 days a week, then you can start adding more kilometers to runs, again no more than 5-10% each time, and a couple weeks adaptation each time.
The biggest thing is to keep it all low key, easy pace mileage. Speed work is not necessary. I wouldn't recommend speedwork until you have been running consistently 5-6 days a week, and have a weekly volume in the 35k+ range. Running speed is more about volume than it is anything else, and for the vast majority of runners, they would get more benefit out of adding more mileage at lower intensity than upping intensity on their current volume.
Safe, steady progressions is much better than trying to add mileage as soon as possible.