I've been there!
It's actually unusual for a male w/ those huge fins to zoom around, unless he's a plakat (short fins). He sounds very healthy!
I channel my worries into API's Master Test Kit. If you order it via Amazon. you can get it for less than $20 (over $35 @ Petcosmart). Indulge in the 24 extra test-tubes you can buy through a supplier on Amazon, too. They only give you 4 glass vials w/ the kit; they break easily in a ceramic sink when rinsing. Also, if you get more than one tank (and I predict you will soon enough) you can perform multiple tank tests w/o cleaning those 4 test tubes again. Also, get a good thermometer and a back-up heater (if it's cold where you live). Also, HAVE MEDICINE ON HAND BEFORE he gets sick! If he should get sick @1:00 AM, it will be hours b/f you will be able to get to a store. Read the threads on sickness in bettas; you'll be able to stock a "first aid kit". From what I've read, Epsom salt is the 1st ingredient in your arsenal, but check on other good potions. You might also want to buy some silicone leak repair to have on hand. Prepare for any disaster- inevitably, if one occurs, it will be when the stores are closed!
One hole in a fin isn't cause for concern, but check all tank decorations. I notice sharp points and rough surfaces on commercial aquarium rocks and plastic decorations. I only use smooth stones in my aquariums. Keep an eye on the hole- it's probably nothing & will heal up.
I keep a 2-gal jug w/treated water and a heater in it at all times. If I need to do a water change, I always have some water of the same temp. on hand.
These precautions should let you be able to sleep at night!!!