I am definitely no expert on this but I do have a few years under my belt of serious running, so here's my advice. Feel free to chime in with suggestions or corrections as you see fit.
There's two big forms of belief out there: minimalist and the basic social or traditionalist runner.
First off, you have to understand the term heel-toe drop. The average Joe-Schmoe running shoe normally has a 12-13mm heel-toe drop. The minimalist shoe is 4-6mm all the way down to a zero heel-toe drop. What this means is the amount of rise or cushion in the heel of the shoe. A 12mm drop is quite elevated where as the zero drop means a completely flat sole (barefoot). The way I like to think about this whole thing and how it pertains to your muscles and gait is to reference it to snowshoes. Have you ever snowshoed with a pair of shoes that have an ascent bar?
What that is is a little metal bar that you can flip up as you climb hills to help reduce calf fatigue. It gives your muscles a break from the strenuous climbing so you don't feel that calf burn. Our sneakers have that ascent bar essentially built in by adding all that rise to our heels (significantly less elevated than the ascent bar but you get the idea). Does it feel good? Sure does, however it's not doing our body any justice and it's disengaging important muscles. This rise also pushes our foot to a more heel-strike gait instead of a more natural fore-foot strike. The ascent bar is awesome on snowshoes but to walk around/run in shoes that elevate your foot like that is no bueno.
There's also the question of "do I need a shoe for pronation, neutral, supination, stabilizing, etc?" In my opinion, unless you have some seriously funky defect I don't think you need to concentrate on finding a specific gait altering shoe. You've got to run in what feels comfortable to you.
Here is an awesome article by RunBlogger describing the emphasis towards a more minimalistic running shoe. His research is all that and a bag of chips.
I used to run in basic road running type shoes. First Asics, then I got turned on to some Brooks Adrenaline. When I ventured onto trails I realized I needed a shoe to handle the terrain better as I felt my foot slopping around in my shoe as it tried to cling to rocks, slide around in dirt, get saturated in rivers, and get beat up by the trail. **I also used to get a lot of knee pain running on roads. After conditioning my body to trails, I almost never ever get knee pain unless you count day six of an eight day trail race averaging 30 miles each day. In that case, every damn thing hurts. I have found trails improve your body in so many ways and completely busts the myth that running is damaging...but that's a whole other topic I could write a novel on.
Here's a great article on trail shoes entitled "Do I really Need a Trail Shoe?"
When I started out on trail I ran in Salomons. I love these shoes but they are super expensive since a lot of the pros wear them and advertise for them. I have since started looking at the more minimalist type of trail shoes as I think that there's some great arguments for reducing all the fluff and cushion in shoes. I am intrigued by barefoot running, however, I think there's something to the fact of having a good amount of protection for our feet. The barefoot advocates stress "in the old days...blah blah blah and the ancient tribe of whatever go barefoot!" but in my opinion, unlike the old days we now have to worry about stepping on crap like nails, glass, and stuff careless people throw on the side of the road and trail. Plus, a good cactus needle, acorn, or rock puncture to the foot is going to put you down for quite awhile...feet don't heal quickly and that shit hurts!!! Not to mention the great potential of breaking or jamming a toe...ick.
WARNING: Seriously disgusting pictures
Yeah, No Thanks... I'll keep my shoes.
So back to minimalist running. I have started wearing Saucony Peregrine shoes and absolutely love them. These shoes have a 4mm hee-toel drop which has made a noticeable difference in my running gait. I didn't consider myself much of a heel-striker before but now I definitely feel a difference with being more on my fore-foot and having a faster turn over rate (faster cadence) when running. They make me feel light and springy in my step! With minimalist shoes you have to take it very slowly though. Your calves, hamstrings, butt, and achilles will be forced to do work they aren't used to doing and you don't want to cause injury. Just as RunBlogger states: I can't stress this part enough. GO SLOW.As with most minimalist trail shoes the Peregrines have a rock plate in the sole to help prevent the bruising and battering the trail will do to your feet. I can't even begin to imagine running barefoot on some of the trails I play on.
My suggestion is: Go to a reputable running store if you have them in your area. Talk to staff that are actual runners (most are) and get their opinion. Don't just listen to one but talk to a few, surf the internet, and get into a store to slip your feet in several. Actually run around the store or outside sidewalk in the shoes to get a feel of them. Be conscious of any spots that rub or feel out of sorts. These spots will be intensified a few miles in. If you're doing trails with hills/mountains leave a little extra room in the toes because that descent is going to make you want to curl your toes back into your heels if they are too small and banging into the toe box. It will reduce you to a crawl, believe me, and you'll lose toenails.
As for Gore-tex (GTX), I tend to stay away from them unless you live in a really rainy state or run a lot in the snow. They are great for keeping wet out if it's a drizzle and you have gators on, but if that wet (river, heavy rain, deep snow) seeps over the tops and into your shoe you're screwed. GTX will hold that water in your shoe like a well sealed boat and you'll be left feeling like you have 5lb weights attached to each leg. Plus, if you're a heavy sweater like me the sweat from your feet will be miserable as you soak through your socks and start causing friction blisters. I have friends who buy GTX running shoes for the winter and love them (they are great insulators for the winters) but, for me, I just wear regular trail shoes, gators, and good wool socks such as Smartwool. It's worked for me for 10-15 mile runs in the snow and ice. Anything more in miles than that and I would consider purchasing a pair of GTX for the winter.
Check out I Run Far for a ton of excellent information as well as gear/shoe reviews.
I'll leave you with these handful of brands that I've heard great things about and have running friends who wear them (RunBlogger lists a handful but most of them I've never heard of and can't say I would recommend):
Saucony (such as Kinvara & Peregrines)
Salomon (XA Pros &XT Wings)- I still love these shoes and feel they are great for long distance foot protection
Brooks (such as Cascadia & Adrenaline)- I still use my Adrenalines for the treadmill but looking into replacing them with some Saucony Kinvaras.
Asics- road shoe
Cheers and Happy Running!