Let's start with the jeans. Go for something darker that will fit his legs nicely and make sure the waist is actually his size. Many fathers I know assume that an extra inch makes them look slimmer. It does not.
Every man's style is a little different, but an oxford shirt is one classic everybody can agree on. It works with denim, chinos and suits any time of year. If your Dad is used to wearing "blousy" shirts, then start with this.
I can't stress the importance of a casual shoe that isn't a super-padded sneaker. That worked for George Banks in Father of the Bride, but he owned a shoe factory. Get pops into some casual lace-ups. Don't let him lose it at the shoes.
You might be rolling your eyes, but a polo is one of the most versatile pieces a man can own. Dad can throw it on for the golf course, under a jacket or just bumming around. Just please, for the love of god, make sure it fits.