So it sounds like you just need to work on you base and you do that by getting in the mileage. No speed work just easy miles.
Ok once you go out and get shoes and you have a 2 and a 3 mile course marked out I would reccomend a 4 day program.
Monday off, Tuesday 2 miles, Wednesday 2 Miles, Thursday 2miles, Friday off, Saturday 3 miles, Off Sunday.
Try that for 2 weeks. You will be amazed on how you will feel, There is no easy way around it, if you want to get faster you have to get the miles in.
Week 3-4
Monday off, Tuesday 2, Wednesday 3 miles, Thursday 2 miles, Friday off, Saturday 4 miles, Off Sunday.
On your days off get some cross training in, riding you bike, sports or even walking. But slowly you build up and you time will come down. When it comes to shoes try going to a running shop you might pay a little more for the shoes but you should end up with a decent pair. Build up slow so you dont injure yourself. Eventually if you do it enough you will learn what to do. If you do that and you need more advice let me know. But make sure you get the mileage in. If you get tired walk one minute and get back to it.