My first Christmas/Birthday wrapping jobs were absolutely horrid. I didn't have any wrapping paper to use and I was scared to buy some and not have anywhere to stash it. You know the tissue paper that comes in shoe boxes? I used that and masking tape to wrap. It wasn't so bad though because I made the entire thing into a big joke so people thought I was funny instead of pathetic haha.
This year I only had one gift to buy and I used a gift bag. I suppose that is a bit of a copout but the person already knew what I had bought, we discussed it beforehand, so it hardly had the element of surprise anyway.
I still hold that if I really wanted to I could do a good job of it, mostly for being such a perfectionist all my life. But who knows!