I think that it really depends on what kind of riding you will be doing on what to get first. I have to agree with the "Get a PUMP and a spare tube. Get a PUMP and a spare tube. Get a PUMP and a spare tube. Get a PUMP and a spare tube." comment, a tire lever set, patch kit, multitool, HELMET for sure but a lot of the other stuff I would kind of see how things went and decide what you need.
Of course if you will be leaving the bike unattended a lock is needed but I have been riding since 2009 and have only needed to lock my bike one time, but thats mainly because I ride on rail trails and random single tracks mostly so.... with that said I do have a small cable lock that I carry in my pack just in case and its been sufficient thus far. water bottle? sure BUT I have a box of water bottles that I don't use right now because I find it more convenient to just shove a Powerade bottle in my cage, I do like I said have a ton of bottles but only one gets used and that is very rarely, I don't think a lot of thought needs to go into a water bottle really, have one but which one doesn't really matter IMHO, start over thinking stuff and you end up with tone of stuff that you don't use
If you plan on riding at night lights will be needed but I wouldn't call them a necessity unless, well.... you are riding at night
In my pack I have
2 bandanas
tire lever set
hex key set
cheapy bike tool (because it has a screw driver on it mainly)
1 tube
patch kit
Leatherman multitool
mini pump
One red, one white Nite Ize spotlit (clipped to my pack for just in case)
air pressure guage
I have only needed a random hex key from my pack for a seat adjustment since I got back into riding BUT I consider myself VERY lucky for that and would never go on a ride without grabbing the pack. but I would recommend the items I mentioned in the first paragraph for starters and see what you need from there, a good floor pump to keep home is a great thing to have also, I usually check pressure before I leave on a ride and the floor pump is nice to have for that.
Good luck with the new bike!