>>136462He's not going to be in wilderness if he's just starting out. Very few people actually go into "wilderness", it's not convienent to get to.
OP: As recommended
>>136402, a hydration bladder is a fantastic piece of equipment. A lot more convienent than water bottles, and usually have enough space for other things without being hueg like backpack. (Get one with a waist strap.)
What other things? ID... drivers license, carry permits, insurance card, maybe a debit/credit card, some cash, phone, house keys, flashlight, etc. Unless your jogs are several hours, I wouldn't worry too much about extra socks or rain gear.
First aid kit. Supplies for minor scrapes/pokes, and some athletic tape if you twist something. Moleskin, because blisters. Bandaids. Just the basic stuff, don't need to go crazy here.
Depending on the wildlife/people in the area, bear spray or defense spray may be something to consider. Handguns are good tools to have in certain situations. (Friend of mine's wife had a mountain lion stalking her on her morning runs last summer. She now carries a 380.)
Don't be one of those runners who's plugged into an ipod or whatever, totally tuned out to the world around you. It's dangerous for you, makes you an easy target, and really annoys others around you.
If you're coming up on someone, a simple "On your left" or "On your right" is appreciated. Especially if they've got a dog, or are on horseback.