Glute soreness and best exercises for tightening glutes?

alsaxon

I am just getting back into working out and I notice again, that although squats are supposed to be great for glutes, I only feel muscle fatique and next day soreness in my hams, quads and inner thighs. I feel nothing in the glutes at all. I notice that when I run hills my glutes are sore. So this is a multipart part question: (1) What exercises target glutes best? (2) Should glutes be really sore or is it just a muscle group that is so large that it can handle more and doesn't necessarily feel sore to prove the exercise is working? (3) when the glutes are sore should it be the entire glute or just the upper? I noticed that when doing hills just my upper glutes are sore not the bottom half (as you approach the thigh). Now that I think about it I'm not sure that I've ever had an entirely sore glute.

With this being said I know soreness will eventually go away, but since I'm new to working out again the soreness the next day or 48 hours following is a good indicator of what's working. So while I have this to clue me in I need to figure out what is working.

Thoughts?