I've never pruned a cucumber plant. Is there some advantage to doing so?

Don't prune the cucumber.
You only transplanted it three weeks ago and it is already blooming? that is pretty quick.
Remember that most of those early flowers are male so it may take another week or so to see female flowers and cucumbers.
I just picked my first cucumber today. I transplanted six weeks ago but it sounds like you are ahead of me.

You don't need to prune your vine unless it gets entirely out of control, size wise. It is going to make side vines. That is normal. It sounds to me like you are doing everything right. Keep at it: consistent moisture, sun, and liquid fertilizer regularly, since it's in a pot. If you have a cage or trellis, you might like that to keep the vine from spreading all over the place. They will grab on with their tendrils, but you may need to help it onto the trellis at first.

Susan2010- I have had mixed opinions. From what I heard, removing the first few buds is supposed to put the plant's energy back into growing the root system/branches/vines, so that it will eventually double your crop. Since there becomes more space on more greenery, you get more blooms and stronger support. Then, the suckers "suck" the energy from the fruit once they start to produce, supposidly. I have also been told though, that if you do it incorrectly or at the wrong time, you will just be removing half your crop! So thats my delema since I dont know the correct way :)

sjkly- yes, I am in shock how quick! Especially compared to my other plants. Your right..I dont think I have seen any females, so I guess I wouldn't be losing any real fruit lol. I heard males make the fruit thick and bitter tho- anyone know if this is true? seems odd.

donnabaskets- thanks, I hope I am doing everything :) I do have somewhat of a home made (kinda ghetto) trellis. I raised the bucket onto a chair so it could run downward instead of up. I had some old fencing I've propped up so it has some support under the vines on it's way down.