Wrapped snacks are fine, as are Ziplocs of snacks you fill up at home. What they question is anything that would appear to be a liquid or a gel-type substance. I don't know where peanut butter would fall on that list, but maybe it's best to leave the Jif at home. 
An empty water bottle is OK, but you can buy water at an airport shop once you're through security, and you can take that water on the plane with you. Other than that, you'd have to find a water fountain or a ladies' room sink, somewhere past the security area, to fill your empty bottle.
Remember to put your other carry-on liquids (shampoo, etc.) in 3 oz. or less bottles, and group them all together in one quart-size Ziploc. Toothpaste is considered a gel, so add a travel-size of that to the
Ziploc. I also put my lipstick, lip gloss, & mascara in that bag
so there'd be no questions asked. Have your Ziploc handy on top of the other things in the carry-on. You'll need to pull it out for the screeners in the baggage x-ray area. I put mine in my bin with my shoes & slide that through the machine behind my carry-on. Sometimes they ask to see the liquids before x-ray, and sometimes with x-ray -- I've run into different methods at different airports.
If you need to take a liquid prescription medicine with you and it's more than 3 oz., keep it in its original bottle with label, and let one of the screeners know before you get to the x-ray area. There will be screeners standing around looking at your boarding pass and asking about liquids and such, before you ever get to the x-ray machine. They can give you a special sticker for your medicine & clear it to go thru.
Biggest problem I had recently with a carry-on was space in the plane. My bag fit the dimensions for carry-on, but the space under the seat ahead of me was partially blocked by some sort of metal box bolted under that seat. So I got all the way over to my window seat, found my bag wouldn't fit, and then had to interrupt the line of other boarding passengers & get a volunteer (man) to hoist my bag into the overhead compartment. The overhead bins usually fill up quickly......and I can imagine now that airlines are starting to charge for checked bags, the overhead space will be at even more of a premium.
One other thing.....if you're flying on a smaller plane, say one with 1 seat on one side of the aisle and 2 on the other, you can keep your carry-on bag with you UNTIL you go to board the plane. Then, if you have a large carry-on (for instance, a small upright suitcase with wheels), they will take it from you "plane-side" (on the jetway, right before you step onto the plane) and put it in the cargo hold. So you will not have access to this bag during the flight. When I flew on a small plane, my purse went on the plane with me, but my upright, wheeled "carry-on" bag had to be checked plane-side. Bear this in mind when you pack anything you really want with you on the plane, if the plane is small. Pack those things in your purse, if possible.
BTW, to get a bag back that's been checked plane-side, you stand around on the jetway, beside the plane's door, right after you get off the plane. In a few minutes, a baggage handler will start bringing up the "carry-on" bags that were checked plane-side. You do not claim those at Baggage Claim.