It's often a good idea to overexpose 2/3 to one full stop to get tighter grain, brighter colors and contrast. In the past I sometimes got blah images if i didn't.
As it's the OPs first ever rolls of film, I'd suggest that he expose it at box speed, and get used to using it, rather than instantly embarking on non standard procedures which he doesn't necessarily understand.
The whole "tighter grain" thing is bogus when compared to slower stocks generally. For example, you will get tighter grain shooting 200t at proper exposure than 500t overexposed by a stop.
Underrating a stock is merely a way of getting the tightest grain out of it. Is it going to make a 500asa stock look like a 200asa? No, but that's not the intention anyway.
Overexposing for tighter grain applies in the world of photochemical finish. You end up pushing more printer light through a thick negative.
By over exposing your image you are placing more of your picture information on the upper part of the characteristic curve, which is where the finer grains are. So your negative appears finer grained whether finished digitally or photochemically.