People have different preferences on grips, from softer to firmer, small to large, I won't tell you what to do that way. However, if the grip is worn and feels slippery, by all means change it to something new. Just starting out, I'd suggest something at the lower end of the price range. You may find that you develop a strong preference as you play more, and it would be a shame to tear of an expensive grip simply because its not the size you want. Also, most grips can now be installed with air, rather than with double-sided grip tape. With that kind of set-up, you can also remove the grip, add (or subtract) layers of tape to change the diameter, and re-install the same grip.
My personal preference has bee for Iomic grips, and I'm also very happy with a Pure DTX grip I had installed on my driver.
Its more about comfort than anything. There really isn't any data proving that the thickness of the grip changes what you do with the club at impact.
If it's a worn out grip that can effect how much grip pressure you use. Besides that, find a grip you like.