The main reason you want a static IP is so that you have a way to reach your cameras when you are away. Picture this, if you had to call someone but didn't have their phone number or it had been changed with no forwarding number to call, how would you reach them? The static IP gives you that same number all time. That said there are other ways to connect from the outside by using some sort of DDNS system.
Since you are going to be using an IP security camera I would recommend a Synology NAS, they have a DDNS system that works quite well and comes with the cost of the NAS purchase and there is no monthly check in that you need to do with some of the free DDNS services. Additionally you can point the camera to record on the NAS, so you get lots of storage and easy expansion and they even have their own App you can use to Access the recordings.
That said you will want to put the NAS behind a router and you can port forward to the NAS. A Netgear WNDR 3700 is rather cost effective and will do the job, the nice thing about that router is that the ports all show up as stealth, even when they are open to port forwarding. So if someone scans your router from the internet they wont even know is it there. If you don't know how to do port forwarding, the Synology NAS can be connected with your custom quick connect code that you setup for yourself.
In the past these NAS devices have been pretty good, they have a compatibility list you should check out, then purchase a camera from that list to work with the NAS, the only thing I will warn you about, the recent DS1815 is somewhat loud when the hard drives are active and it might be that is true with the other models of 2015, so keep that in mind when deciding to get the NAS and where you want to place it. I use WD Red HDDs and they work great, since you will be recording video, it might be a good idea to go with the WD RED Pro hard drives, they are faster and reportedly quieter.
Once you are all setup don't roll out updates automatically, monitor when an update comes out, it will tell you in the web management interface, I think you can set up the NAS to email you as well for that, then check the Synology forum to see what other users have for experiences with the update and you can even ask questions of others to see if they have a certain web cam and NAS and if they were good with the update. Not every update Synology rolls out is perfect, but as long as you are careful you should be pretty smooth sailing with the NAS.
I will paste a link to the site and you can decide for your self.
I hope this helps you out