Before I started getting serious about running, last year sometime, I didn't really put much thought into my "equipment" for running besides my shoes. While shoes are very important I have come to find having specialty clothes exclusive for my running makes a large difference. As the distance I've gone had increased so has problems I've heard runners frequently encounter. Luckily I haven't had too many of the more nasty issues like toenails falling off, but chaffing is a real issue. AKA chub rub. Another issue I've had with "regular" clothes is the constant pulling and tugging that I used to do to keep my clothes down and covering my bouncing flab. Yeah, it's not attractive to have half my stomach in all it's glory. I'd rather have it covered, thanks, no wardrobe malfunctions wanted!
Above all, though, I would want other runners athletes, and weekend warriors to find what works best for them. What works for me may or may not work for you. But I hope this list is helpful to others who are looking for somewhere to start.
The most basic is what you actually wear. What I would wear on a training run is the same I'd wear out to a race. Namely I've come to LOVE running tights. I originally was a little hesitant about having a raging camel toe but it's not too bad. Yes, they're tight and with tight comes some spillage but it's worth it for the comfort. I like the Adidas Capri running tights. I like them because they hug and they don't slip down while I'm running. Since I have a dunlap (you know, when your stomach dun lapped your pants) it's pretty important to find something that will stay up while I'm running.
As for shirts I actually like plain t's. I get a little chaffing under my arms with them but it's worth it IMO. It's hard to find wicking fabric shirts that don't ride up while I run. Nike's pro sports ones come close but they show every last drop of rolls I've got. Yeah... so for races I like "inspirational" shirts. My favorite that I wear a LOT says "Strong, Beautiful, ME". I'm sure if you've been on my facebook page or know me in life you've seen it. Other than inspirational shirts I like the walmart Danskin Now yoga line for shirts. I wear a sports bra underneath but I like to look somewhat cute when I run. Well as cute as a hippo charging after you can possibly look.
As I stated before shoes are of the utmost importance. I haven't really gotten into minimalist running although I'm starting to. You want to make sure that your shoes are flexible and can bend when you bend them. Shoes that do not bend when you try to fold them in half are too cushioned for runners. Although I'm sure there are many runners who uses as my friend calls them "Cushiony beasts" they don't promote proper form. I like Nikes to run mostly. Although I have used both New Balance and Sauccony. Go to a running store and have them evaluate you for shoes, this will be your best chance to get the best fit for your stride. My next step will be to try vibrams 5 fingers or the Skeletoes. I haven't gotten that brave yet!
For the ladies bras are pretty important. Don't want to get a black eye. Now I'm not very well endowed so I have a lot more options out there than many others. But to keep it brief I like two kinds of bras. Either the Danskin Now high impact sports bras that zip up the middle OR the Adidas sports bras for high impact. I like those puppys to stay in place!
Anything other than what I've already explained are "extra". They're nice to have but definitly not essential. I love head wraps. I use the Nike sweat bands. They keep my hair in place and sweat out of my face!
Socks can be pretty important as well. I like the Adida's brand for socks they kind of grip in the middle so your socks don't come falling down!
Now I went for a while on the search for the perfect earbuds that weren't going to cost an arm and leg. The ones I've found work the best you can get from Walmart (I'm sure you have found out by now I like Walmart HA!) They're Philips brand and they have earhooks. About $17 at walmart!
My parting advice here is to do what works for you. If you're lost in the woods use what I've outlined as a base but don't be afraid to try new things. Every body and running type is different. So branch out, try something new, and you may find your runs to be a bit easier!