So, one of the big issues you are likely to run into (Even if you aren't paying for your own power) is noise. Some of these rackmount servers not only run hot, but they also run loud, very loud!
Does the server need to be rackmount for a particular reason? Or could a desktop server work just as well?
Either way, you probably want to be looking at the following types of server if you want something mainstream from one of the big brands (E.g. with IPMI, iDRAC or iLO)
- HPE DL380 G9/G10/G11
- HPE ML350 G9/G10/G11
- Dell R730/R740/R750
- Dell R530/R540/R550
- Dell T330/T340/T350
- Dell T630/T640/T650
There are other brands out there, for the rackmounts I would stick to anything which is 2/3U in size as they normally have larger fans and as such are quieter on power up and general running. Likewise they also generally have more ports for expansion if you are looking into addings bits such as other drive cages, RAID/HBA cards etc
For the brands, Dell can sometimes be better than HP for getting updated versions of iDRAC and firmware updates as HPE love to lock their firmware, BIOS, Inteligent Provisioning and iLO updates behind an account paywall.
You mentioned Plex, one thing to note is that if you are running Plex inside a VM then it won't be able to take advantage of the hardware encoding on the server so you are likely to see very high CPU utilisation, I had a similar issue with my setup and in the end I opted to get a cheap NUC solely to run Emby on so it could leverage the N100s quick step technology whilst the files were held on a VM on my main server setup.
For the rest of the stuff which you are running it also doesn't sound like it is going to need a insane amount of CPU grunt either so most servers should be fine, the reasons I would steer aware from stuff older than the G9 and X30 series from Dell is they are getting a bit older now and support is starting to be bulled from Windows and ESXi versions for them (If you are using Linux it shouldn't be too much of an issue but I'd say within the past 3-4 generations).
For the network switch, anything which supports VLANing will likely be sufficient for what you are doing unles you really want to get into setting up things such as "router on a stick" or getting the switch to hand out DHCP etc. The networking part of the forum may be able to help a bit more but personally I'd pick up something like a HP 1820/1920 unit as they are rock solid and if they are part of the old series they have a lifetime warranty as well.
On the OPNSense router, you could potentially run this in a VM on your servers which are setting up, that is what I did for quite a long time and it worked good enough until I wanted to split it out into its own hardware to avoid it being dependent on the servers.
For the rack, I would say this depends if you decide to go full rackmount everything or if you instead go for a desktop server and then only rack mount the network kit, you can sometimes pick up a few deals on various auction sites where companies are clearing out their old kit or if you want new those same sites have some not terrible deals for ordering small and larger racks.
If your budget is really tight an IKEA Lack cable can be used to hold a rack mount server, not multiple (Without re-enforcement) but for the odd one and a switch it will hold up until you can get something more substantial