Okay, nobody offered. You did some work to start a conversation, so here's something, anyway. Running shoes are not well understood. A lot of research shows that wearing running shoes is a bad idea to start with, because the arch supports and cushioning over time weakens the muscles of the foot. Running barefoot or in sandal-like shoes, as humans did for most of our history, preserves the natural arch and strengthens the muscles. But, we don't run on soft soil anymore, we run largely on paved surfaces, and running barefoot on these or in so-called minimalist shoes will lead to mashed feet and plantar fasciitis. It would be nice if we could all go back to when we first started running in those over-padded shoes and not do it, but once you start using them, your feet can't just go back to running barefoot again -- you would have to build the muscles back up slowly. But as long as we're going to run on treadmills and pavement and not on grass and dirt, we'll probably need those padded shoes and not the minimalist approach. Okay, at least someone said something.
It's hard to offer running shoe advice because everyone's feet (and legs and hips, and how they walk and run) are different, and what works well for one person might not work well for someone else.
As someone who has consistently run about 30 to 50 miles a week for the past 17-18 years (recently it is 60 miles plus for marathon training), I have gone through a lot of running shoes. I have had most of the normal overuse running related problems in the past (probable stress fracture in foot, shin splints, achilles tendonitis, runners knee, IT band problems, hamstring issues) - but I wouldn't blame those on bad running shoes as much as training too much or increasing mileage too quickly, lack of experience, and part of the running learning process is learning when little problems might become bigger problems and the need for pulling back a bit before they do become bigger problems.
I think if you are just starting running, going to a specialty running store and having a running shoes specialist fit you is a great idea. I have never done that, and I usually pick running shoes by trying them on, bouncing up and down a few times, and deciding if they feel right or not. I still do this.
About two years ago I switched from a shoe with a lot of cushioning to one with slightly less cushioning, and so far I have felt much better in those on runs and have not had any running related injuries despite ramping up my mileage. Some people need more cushioning though, and some people do better with "barefoot" running shoes. I look for shoes where I have a little extra space in the toes (toes not near touching the front of the shoe), and some shoes are wider in the forefoot than others. A lot of people need some room for the toes to spread out a bit when they run, and for me it has been trial and error finding what works. (Error ends up with damaged toenails and other misfortunes on 20 mile plus runs).
I think probably the biggest impact for me when I switched from a lot of cushioning to slightly less cushioning is that I stopped "overstriding"(foot lands in front of the hip), and while I now take probably smaller strides, my foot lands directly beneath my hips, and seems to be working out well for me with fewer running injuries. (Sometimes I trip on sidewalks or fall while walking over a curb while running and twist my ankle, but that isn't necessarily a "running" injury).
I also go through shoes pretty quickly (I am training for my second marathon this year, I'm up to 260 miles a month, and most shoes last about 300-500 miles, so I can't afford to replace costly shoes every 1.5 - 2 months). I look for shoes that are below $100, and usually go for the older, usually marked down model instead of the newest, current model. I do make sure to buy shoes specifically designed for running - and so far what works for me for running has always been around the $80-120 price range before being marked down. My sister (who runs slightly less than me) has had the same expensive ($150 plus) pair of running shoes for years and swears by them, but I tend to wear shoes out pretty quickly. (I know my shoes are toast when I start having random foot or knee pain).
I am on my 8th or 9th pair of running shoes that are same style shoe (although different models because those seem to change every year), and I keep getting more of the same style because I feel great running in them. I'm open to trying different shoes, but since I know what works for me, I stick with that.
Towards the very bottom of my list is color. Most styles of shoes come in a variety of colors, and I usually go with what is cheapest, although I tend to like very brightly colored running shoes for visibility reasons. There are certain colors (tan/beige/completely black) that just don't fit with what I like and I'll avoid, even if they are super cheap. I mention this, because if you have shoes that you like to look at or go well with an outfit, it might encourage you to get out the door more often.
As for whether barefoot running versus modern cushioned running shoes are better - that's a whole debate in itself. A large part of running is the ability for the foot (arch) to flatten and then spring back as you run which propels you forward, so high arch supports can inhibit this spring like motion, and forces that are absorbed in the feet end up being absorbed in other places like knees and hips. But just because a shoe has some cushioning doesn't mean it is inhibiting this springlike motion. Many people are natural heel strikers, and while there is some debate as to whether heel striking or forefoot striking is "the correct way to run", both are natural ways of running and one isn't necessarily "wrong". So running with shoes on with a lot of padding or minimalist shoes are both fine but might not work for everyone. There are many elite runners from Africa that grow up running barefoot and switch to shoes as they become professionals - I'm not sure how much "strength in the foot" is lost switching to shoes as long as foot is allowed to spring like it should. (Mine still springs, even in my moderately cushioned shoes).
I think people getting out and running in general is great, especially if you have never run before. Find shoes that are comfortable, affordable, and that you like to wear when you run and then go out and run. If you are just beginning running don't be intimidated and just try and see what works for you.