Happy to help. First off, no attorney needed. I met with one and after a few minutes, he admitted a lawyer isn't necessary, so I submitted on my own.
So if it's your mom's grandfather, you would need:
Your birth cert
mom's birth cert
mom's marriage cert if her name changed from her birth cert
mom's parent's birth cert
mom's grandfather's birth doc/baptismal doc if possible
those are the minimum docs. I also submitted a few supplemental docs (but as my lineage was all maternal, marriage certs became necessary) that you may want to: Census docs from Canada and the US as both list birth place. Death certs don't mean a ton, because those are just filled out with whatever someone says.
as my lineage is all Quebec, I'm not sure about NB in particular. Quebec didnt issue birth certs in the 1800s, but god bless the catholic church for their baptismal records, we got a certified copy of it from BANQ.
Timeline: About a year if you are non urgent and apply now-ish. Seems to be getting a little longer as more americans apply.
Highly recommend checking out
https://www.reddit.com/r/Canadiancitizenship/
This is an incredibly helpful sub, you'll be able to find NB specific info too. They'll have examples of packets submitted, how to answer every ? on the app, etc. Start at "Start here"
I will also say that online records tend to have more than you think; between familysearch, ancestry, and some sites that get you census data, you can get a lot of it printed off even if you're waiting for "official" certified copies of something.
app cost is $75CAD per person, plus whatever cost is for some very specific photos (mine was like $20) plus whatever you may have to pay for certified copies of docs