For sure ditch the gloves!
I'm not about to tell you not to get straps, as I use them myself on my last two heavy deadlift sets, as I don't like having one of my arms palm out with the weight I use. That is the ONLY exercise I use straps on though. The rest I use good old chalk. For the longest time I didn't believe chalk could make that much of a difference in your grip. I used to use straps on all kinds of exercises (pulldowns, rows, etc.) but one day I decided to pick up some chalk and give it a try. I've never looked back!