No.. Not at all.
$800-850 IIRC
We just have a few OVH dedis; s1/s2 both have a 7700k/32 GB RAM/SSD from their older "GAME" lineup- looks like they just recently replaced those with Ryzen CPUs.
@Noahhh! TBH either way, you're probably better off just using some cloud provider. For small servers, the majority of games aren't going to require anywhere close to what you've listed as hardware. If you just want a small server, you can pretty easily and cheaply grab a small VPS from OVH, Digital Ocean, Vultr, etc (things get a little bit more complex if you require windows server, but you can still do it far cheaper than building and maintaining your own hardware)- I might be able to help hook you up with something if you send me a PM.
Another factor that you're ignoring entirely is the internet connection and uptime requirements of the server. I'm not sure what the quality of your connection is, but in most cases a datacenter will offer better bandwidth and latency and also provide guarantees of uptime (and sometimes refund you some amount when they fail). If this is in your house, it's far more likely that your internet will be not great or that your power is more likely to fail. If you just want to run a small server for some friends occasionally, this is fine, but anything past that, it's less than ideal. Also consider that if it's on your network and somebody decides to boot it off, you're pretty much fucked. OVH, for example, won't flinch.
If you need more than a VPS and/or want raw hardware, you'll want to find a dedi. OVH is what we use, but might be too much for what you need. Checkout lower end providers like kimsufi. You can sometimes find good deals here.