Adrian,
Welcome to the community!
I have been on my journey for about 8 months now. I will tell you for what it is worth, that many times over the years I have tried to do the same thing, but have gone out and tried walk/running right away. I would always get discouraged because I would not be able to go far and would feel like I was going to die. This may not be the same experience for others, but I learned I couldn't start out that way.
This time I did it completely different. I started eating less immediately. After one week I started walking 6 days a week (I chose early morning before my wife and kids were even awake) I did this for almost 2 months before I even tried to run. After those 2 months I would run for a couple hundred yards and then walk the rest. I finally moved to a treadmill where I could gage my speed and was able to run a lot further without falling over

That gave me the confidence that I could do it. I just kept adding speed and distance and eventually moved back out to the road. The last thing I did was run a 10k race. I hurt my leg shortly thereafter so I am healing right now. Once I am done healing I am going to start training for a half marathon in the spring.
I said all that to say - if I would have started off trying to run again I probably would have quit long time ago, but because I built up slowly I was able to see progress and maintain a constant workout without feeling overwhelmed and inadequate. I instead built confidence every step of the way. I think it was paramount to my success - starting out slow!
I would suggest joining the running groups here in the forums, they have helped me out a lot along the way.
As for shoes, I know price can sometimes be an issue, but I started having a lot of problems with my knees and feet when I started running on the road (the treadmill was much more forgiving) and I had shoes that were about $70. I really wanted to run so I searched out a shoe store that actually watched me run and looked at my old shoes etc. They actually fit me for shoes and sold me inserts as well. It was $$, but well worth it because I wouldn't be still running if I didn't get them. There are a lot of people on these forums and other running forums that will tell you the same thing. I got mine done at Fleet Feeet
www.fleetfeet.com and I know there are a lot of other shoe/running stores that do the same. Here is an explaination of what they do at these types of stores:
www.bigpeachrunningco.com/fitprocess.cfm
Good luck and Welcome!!