I did this to become an Italian citizen. I did it myself with some help and followed the guidelines issued by the Italian consulate.
In order to qualify, I had to show that my Italian "blood" passed uninterrupted from my grandparents to me, which can be tricky if your grandparents or parents were naturalized. So my first piece of advice is to 100% confirm that you qualify for citizenship before you get too far.
The paper chase took years. I used a service that I found online to obtain copies of all of their birth certificates and marriage certificates from their respective cities. That was reasonably fast and cheap. Getting all the US documents (birth, marriage, death, grandfather's naturalization) was painful. At least for Italy, these need to be the kind of record for which the state is willing to issue an apostille, which is a hyped up certification. There was a lot of requesting state records, getting them, making sure they were the right kind and resubmitting them to some other state office to get the apostille and then having them translated by a translator certified by the Italian consulate. This could have gone faster if I was more diligent, but no matter what, there is a lot of waiting on clerks offices to open their mail and respond.
The application itself was pretty simple. I did this 10 or so years ago and the wait to get a passport was less than a year. Now it's much, much, much longer for Italy.
I had a lot of fun doing this and I think you can do it for yourself. The paper chase was long and slow but the out of pocket cost was modest. If you have the time and the interest, and aren't in a rush, I'd do it. Depending on your situation, your kids can also benefit by being able to work and live in the EU.
BR