So once one reaches Sky Haven Temple one can speak to Delphine about bringing one of one's followers to initiate them into the Blades, why would one do this? What are the benefits of bringing one's followers to the blades? Can any follower be brought to the blades or does this only apply to certain followers.

Eventually, once you bring three, you go on a little dragonslaying excursion and then afterwards can then get Esbern to offer to make a little something for you: a potion that lessens physical damage from dragons (once you get some reqesite ingredients).

Make sure you do it before...

So does it matter who one brings? What happens to the followers once they are members of the Blades?

I haven't tried, but I imagine they are no longer recruitable once the above spoiler'd conditions are met. They still are as long as you're in the Blades' good graces.

The followers I've brought to her are still available for me to take along with me afterwards. Plus, they get outfitted in full Blade's armor.

If I take followers such as Housecarls and whatnot will they remain at the temple or will they return to wherever they come from?

The housecarls will remain at the temple unless you marry them - then they remain at the house of your choice. Derkeethus will constantly run back and forth between the temple and his home in Darkwater Crossing, though. I always run into him on the road in his Blades gear...

I've yet to reach that point, however, so it might be best to just sign up disposable wimps (Faendal, Sven, Roggi, etc.) to The Blades and not lose any worthy warriors to them.

Well , I use them now to take 3 random followers and have them in a place I don't have to remember where I met them.Like some of the followers you brawl with in a random town you don't usually frequent alot etc. As far as the blades themselves , most of the "bad" you heard/read is just the fact they don't really seem done , or at the very least doing the things they just told you they were sworn to do. If you're interested in if these followers are still recruitable after refusing to kill paarthurnax and the blades turn on you , I can check on a character that I did this with , but as of right now just have never set foot back in the place to see for myself.

The game guide says and I quote, "Protect any Blades you wish to see live to fight another day; once Blades (your old followers) die during battle, they cannot be replaced.

Sounds like you do not want to waste anyone good here, so bring only people you don't care about if you really want to do this.

I am on my first playthrough on Master, and I like the idea of 3 people helping me kill a dragon. Dragons are HARD on Master.

only followers who want to be blades says yes when asked by delphine

i think sven will say no