First of all, you should always carry lip scrub, it does not matter if it is summer or winter. Lips get chapped all year round, every person should always have soft and healthy lips.
Just for basics you should have a combo lip product like the Revlon Lip Butters; they are chap stick, lipstick, and lip gloss in one plastic tube. It also helps that they come in most colors we can think of. I would say go with a sweet color, like a pink hue, that you can wear everyday without thinking twice. I prefer the Sweet Tart at the moment because it is very easy to wear in the morning if I happen to forget to put lipstick on at home.
Then, a basic gloss for those days where you don't really want any color and don't want to look like a hot mess. The Nivea "A Kiss of Shine Natural Look Glossy Lip Care" is very moisturizing without being too overwhelming and shiny. It also has SPF 15, which never hurts.
Lastly, every girl should have a "fancy" lipstick. The M.A.C. Ruby Woo is a nice matte bright red for all your night time and fancy outing needs. Since it is a matte color, it lasts all day but tends to get a little dry but it is nothing a little gloss will not fix. Or, you can just re-apply. When I discovered it, it quickly became a favorite (Favorites: December).
It is not quite a long list of things but when you are running around...ain't nobody got time to look through a make-up bag for the "right" lip product of the day. Hopefully, my basic products on the go will save you time deciding what to take with you especially if something comes up last minute.