IT depends on what you want.
If you want 1 cent for each one then take them to the nearest bank that has a coin counter.
If you want to keep wheaties, then sort them out.
This is a great time to start a collection though. And if there are a bunch of you then you could all start a collection. I am guessing that you are worried that there may be some valuable pennies and you don't want to waste any potential profitability. You need to also consider your time. This is a lot of pennies. If there is a 1943 copper cent in there then whatever time you spend is worth it but don't count on that.
If you are interested in putting together a cool collection and don't mind spending the time then this is what I suggest. (Remember, this can be quality time with the family. Treasure is what we make of it.)
We are trying to keep from picking up a penny, finding it in the book, deciding, picking another penny... So, sort them all by decade. Then by date and mint mark. Now check the book. If the book identifies, say 1972D as having some double dates then you know what to look for there. Have each person that is making a collection pick their favorite from each date and mint mark. If you are doing this then it can make sense to pick up penny books before you start.
Some things to expect: Some kids (and adults) get into this and some don't. If you find that you have to press to keep another person involved (or even yourself) then perhaps this is not for them (or you).
Ben (from the post above) does not think that memorial pennies are worth the time. That's fine for Ben. You may think otherwise.
It seems to me that when you started this your goal was to fill the jar with pennies. Perhaps what you should really do is cap it and keep it. You reached that goal. Celebrate. Then start another bottle with nickles...