First off, congratulations on deciding to become a runner and signing up for your first half! It sounds like you have a really good plan in place to gradually build up to the distance. Good job!!!
As far as the shoes go, I can't help much outside of saying that minimalist or barefoot shoes will give you a more natural stride and supporters of them will probably say they don't cause additional joint impact, but I know there is a lot of information out there that supports AND detracts from that statement. I really think a lot of it comes down to an individual perspective and what works for YOU.
But I will say that I highly recommend you go to a running-specific store and get fitted for your type of running shoe that will be best for you. If you go to a specialty store the technician will watch you run and evaluate your stride, whether you over or under pronate, your arch type and more and then make recommendations for what kind of shoe to use. They should be able to answer questions about minimalist shoes too.
But if it were me, I would ditch running in cross trainers as they are not made for that activity and will have different features built in, although they should be okay for now while you are still in your early stages if you can't get running shoes right away. As you may have already seen if you've done a google search or anything - there is a TON of conflicting information about running shoes out there and each person is an science experiment of one. :-)
Find what works for YOU and then...well, RUN with it!!
Best wishes to you on this journey!! Glad you're part of the running "family"!
So, my family has convinced me to train for a half marathon (Disney princess 1/2 marathon in February 2014). I know, that's a big goal for someone with no running experience and quite a bit of weight to lose, but I thought why not? We are a... "fluffy" family, but my ~55 year old aunt (also with no running experience before training) ran her first last year, which convinced me that if I put my mind to it. So far, 3 weeks into training for step 1 (5K) and enjoying my peaceful mornings, and my dog is enjoying the jogs. Right now, I am using the ease into 5K app for android, which is 30 minutes of run/walk intervals. I do that 3 days weekly and as soon as I start work (where they provide a gym membership for me), I plan on swimming the opposite 3 days a week to improve my cardiovascular endurance while being gentler on my joints.
So I have a dilemma. I have 2 pairs of shoes. One is a pair of New Balance 990s (crosstrainers) and the other is a pair of Merell Run Trail Glove shoes. In the cushier shoes, I definitely have a heel-strike stride, which makes me pick up my toes more and causes shin pain. The barefoot shoes definitely make me feel like I have a more natural stride, but I'm concerned that no padding will cause joint problems long-term.
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