Mining

Branch mining is the most efficient. There's a mathematical analysis on it in the official forums (the link is to an archive of the post).

Here's a brief description of branch mining:

• You dig down to the bedrock, because that's where you're going to find the most different kinds of stuff.
• One or two layers above the bedrock, so you don't have it interfering with your work, you dig a long tunnel, 2 high and 1 wide, which will serve as the trunk.
• Then, every 4 squares on either side of the trunk, you dig perpendicular tunnels extending out 20 blocks (or as far as you want).
• You leave 3 undug blocks between because veins are generally 2x2 horizontally, so you will see ore in the vein even though there is technically one row of unexplored blocks.
• When you finish that layer, you can start one a layer above, offsetting the branches by one block so that you are more likely to find veins you could possibly have missed the first time.

So essentially, a long hallway (the trunk) with perpendicular hallways (the branches) coming off either side.

██▒▒▒▒▒▒  ██ blocks you should mine
██▒▒▒▒▒▒  ▒▒ blocks you can see
▒▒▒▒██▒▒  __ blocks you can't see if you don't mine ▒▒ blocks (there's none!)
▒▒▒▒██▒▒  Repeat this pattern as many times as needed

From a head on view

Travel

As with any mine, travel is most easily accomplished using minecarts.

You can place a booster to get your cart traveling at max speed in a short distance so that you can make the trip up quickly, and you can even attach chests to mine carts to carry all your findings from the mine up the track very quickly.

Short of minecarts, make sure you're using stairs and ladders to their fullest potential. You don't want to be jumping up one block at a time all the way from your mine to your base.

You are standing 32 blocks away. Mobs spawn when you are at least 24 blocks away, but then despawn over time when they are 32 blocks or more away. The other thing is, you're standing at Y = 78. I'm willing to bet that you're within 128 blocks (spherical) of some caves somewhere, which are likely filling up with mobs (there are thousands of spawning spots in caves vs. likely a few hundred in your mob spawner), and they are keeping mobs from spawning in your trap. Between this and the fact that you are 32 blocks away means it is likely that the few mobs that are spawning could despawn before you have a chance to kill them. Finally, mobs freeze (don't move) when you are around 30 blocks away, so unless your pads are small, the mobs will stop walking before they walk off the edge into your water streams, assuming you're using that style of mob trap. This means they will stand up there till they despawn.

Recommendations: use small (3x3) spawning pads, with water streams in 2-block-deep trenches between them, and make it small enough that the mobs are quickly funneled into your trap before they have a chance to despawn. Etho has a very simple mob trap design that is easy to build, expandable, and efficient, and has remained so since he designed it over 2 years ago. I would stand somewhere at least 24 blocks away horizontally, around midway up the spawner and at least 128 blocks away from any caves that aren't lit up. Since mobs do walk around for a few seconds before freezing, with this mob farm, the mobs are funneled into your trap before they have much chance to despawn, so being over 32 blocks from some pads isn't a problem.