There are a lot of general kits available, search on Amazon or some of the survival or surplus sites. Really depends on how prepared you want to be.
I bought a bag and made up my own kit with things more far ranging than bandaids. Suture kit, quick clot, splints, and many more things. Got lots of ideas from a SAR person. I continue to upgrade as ideas come to me.
If you want a decent kit that's ready to go and not too expensive, the Hart medical or Adventure Medical Kit FAKs at REI are pretty reasonable. Just pick one that fits your family size and/or trip duration.
Another way to think about it is what are you willing to fix?
If your medical skills stop after cleaning and bandaging, get some antiseptic and bandages and painkillers.
How about itches & burns? are you any good applying creams? There are some that work and are worth having.
What do you think when you read the back of a bag of Quick-Clot? Do you have the presence of mind to throw on some gloves and try and stop serious bleeding?
splints--how do those work? Sutures? CPR? Epipen?
Having a good kit is the easy part of being prepared. Once you make or get one it will only work if you know how to use it.
Figuring out how to get to it and into it one handed is not a bad thing to try before you need it either.
Right now at Costco (at least mine here in CA) there is a first aid kit for $25 that (in my opinion) is a good deal for a basic "boo boo kit". Its got all the basics and it comes in a folding hard plastic case. If you wanted to, you could pull out the most useful ingredients and put them into a soft MOLLE type pouch that could be stored in the vehicle more easily. I tend to roll my own, but I also carry a first responders trauma kit (with sutures, intubation kit, clotting bandages, splints, pain meds, staple gun, etc).
I'll second the REI packs. I probably own 4 or 5 of them and they stay with the gear that is used for that activity - for example, a small one stays in my mountain biking bag and a larger one is in my hunting backpack.
Note that if you roll your own (or buy pre-made sets) don't go cheap on the bandages - especially the adhesive bandages (which lets face it, get used 90% of the time vs, 10% for everything else). There is nothing worse than crappy band-aids that won't stick or leave a gummy residue!