VPS host (I haven't done this before, it looks like racknerd may be way to go?). I assume I will probably only need 1GB of memory as it will just be a static webserver but that may be too little, not 100% sure.
Never heard of this ISP, but 1GB will be plenty for a static website, or a rather light-weight web application like WordPress. Most VPS hosts allow you to upgrade your machine in-place, by adding additional memory, disk space, or CPUs (to a degree. At some point you will be forced to transition to a dedicated server, or to spread things like storage to a more specialized object storage host)
Email host. This is one of two real reasons I want to own the domain, we have multiple uses for email but currently everything is under one gmail address and a lot gets lost in the clutter. A few people in our org would like to stick with gmail but I am open to other suggestions. Definitely do not want to deal with self hosting on this.
Probably the right choice. I do self-host email, and with things like Mail-In-A-Box it is not awful to set-up, but it requires its own VPS (so you're paying anyway) and the IP ranges of VPS providers tend to rank poorly in heuristic counter-spam systems (because people's neglected / amateur shit routinely gets hacked and turned into spam bots).
If using email for organizing, custody and jurisdiction of the email server should be an important consideration. Anything is better than Google, but there are still shortcomings of hosting email on a VPS or a dedicated service (like, they could still receive a subpoena or search warrant without your knowledge, though they are less likely to be directly collaborating in dragnet surveillance or various classified "counter-terrorism" programs like Google or Microsoft). End-to-end encryption should be used for anything sensitive, regardless of who has custody of the physical server.
Website builder. I plan to use an Ubuntu server with the LEMP stack on the VPS, should I just use Wordpress? I am definitely not experienced in website building so it's not realistic to do my own HTTP. My only concern is using Wordpress will result in a poorly optimized site that may strain my limited resources, but there are also a few people in our org that have experience with it so that would help.
WordPress is okay, but it has a iffy reputation. It is a very popular web application, and is a popular target for exploits as a result. A lot of people set it up and never think about it again for months/years. Like any piece of web-facing software, you need to keep on top of updates and make sure it is not misconfigured. I have not hosted WordPress in a long time, but if you read the HTTP access logs on any VPS you will see dozens of bots probing and attempting to exploit WordPress installations (along with other popular web applications).
You can configure something like fail2ban to mitigate this noise somewhat. Along those lines, you also should exclusively use key-based SSH access. Disable password authentication completely and have fail2ban throw all the bots into the oubliette. If you're extra paranoid, you can use a smart card (like a YubiKey) to store your SSH secret, so it cannot be exfiltrated from your personal computer.