Billy, a couple of questions:
1. Do you want to solve as fast as you possibly can, or do you just want to learn a method you can do every time "reasonably quickly" ? If you want to be really fast, unfortunately, you'll need to learn a good handful of last layer algs. You're probably doing an 8 look last layer currently, which requires 6, 7, or 8 algs depending upon how you learned it.
If you just want to be able to solve the cube reliably and "reasonably quickly" (like 1 to 2 minutes), the 8355 method might be worth looking into for you. There was a recent thread here about it, so you can find it with a search. It's a very elegant method IMHO. Not the fastest by any means, but very nice. It requires only one algorithm for the entire solve!
2. When doing the LL corners, you say it takes a long time. In the worst case scenario you should only have to execute two corner cycles. That's when you have the case with a diagonal corner swap. Can you explain further?
Regarding OLL and PLL: You say you don't understand and ask which one to learn first. Here's a quickie explanation:
OLL is the part where you make the LL all the same color by flipping over the edges and corners.
PLL is the last step(s) where you move the corners and edges to their proper locations.
You're already doing both OLL and PLL... just in several steps each. When you learn full PLL (all 21 algs) you'll do that step by using only one alg. Same thing for OLL: When you learn full OLL (57 algs), you'll do that step by executing only one of the algs.
So what to learn first? First master the LL method you are using now. Then learn 2 look PLL and 2 look OLL. That'll require you to learn approximately 12 new algs. But when you're done, you'll do OLL with only 2 algs, and PLL with only 2 more. Once you've got that down pat, you can move on to learning full PLL, which is 14 more algs.
At that point, you're probably best to wait until you are quite fast before learning full OLL. It's a LOT of algs, and only shaves 2 to 4 seconds off of your solve. I still haven't learned it and don't plan to unless my times really, really drop.
Hope this helped.
Brian.