In terms of gear and equipment to carry that has already been mentioned, not much else to add but to carry a 1/2 roll of TP. Do enough bike riding and some day, having the TP for yourself or SO, will be very useful.

I carry all my gear in a rack trunk bag which are available on REI, MEC and other related sites. The great thing about these bags, such as the one I have, is that it mult-compartment and holds plenty of bike repair gear, wallet, keys, glasses etc and a small pump. Depending on how much gear you carry, there is room for a 1L water bottle and a smaller 750ml bottle. I prefer carrying the water in this way as it keeps the water bottle out of the hot direct summer sun and less subject to having to drink warm water on a hot day.

If your SO is biking with you, having the same bag on his/her bike gives more then enough storage such as carrying more water, lunch and snacks for a long day of riding.

My trunk bag attaches to the rack via Velcro straps which makes for easy removal so it does not get stolen if I need to leave the bike unattended. Also the straps can be used to carry the bag, backpack style.

If your looking to do overnight or multi-day rides, panniers are a must.