Loli_Swat

If you feel like it needs more memory (which unmodded Mincraft apparently doesn't), you can change a setting:
https://cubedhost.com/help/en/articles/1648388-how-do-i-allocate-more-memory-to-my-minecraft-launcher-client-side

Well your goals here surpass the "average Joe's" Minecraft server. What you're describing is more enterprise Minecraft server building, as silly as that sounds.
I personally run three separate Minecraft servers on an old Lenovo ThinkServer RS140 and all three run smoothly. It's running an Intel Xeon E3-1200 with 2x8GB Crucial DDR3-1600. Some SSDs are crucial for world data, in my opinion, because having multiple players loading different chunks all at once takes a toll on HDDs. So much so that I actually installed the world border plugin and pre-rendered a huge circle area around spawn. Took about two days to render, but no more laggy chunk loading!
 
To answer some of your questions, here are my opinions:
Cores and threads don't really matter because Minecraft servers still run on Java, and as far as I know they only use a single core for the server and the rest are for garbage collection (someone fact check me?). With this in mind, the faster your CPU the better. Definitely go with server CPUs, though. Even with an old Xeon E3-1200, my three Minecraft servers run smooth. AMD or Intel is beyond me, though, but I presume team blue has the better server CPUs.
Different people have different results with RAM. For me, the highest end MC server I ever ran had about 20 plugins and 10 active users, and the most I gave it was 4GB and it ran perfectly fine. Plugins arguably take up the most RAM, so the more plugins you have the more RAM you'll need. For players it just depends, but I'd assume that for every 10 players you'd need a gig of RAM. Server-specific RAM with ECC is recommended but not necessary. Speed is to your discretion and depends on your CPU, but I'd try and get the fastest RAM possible if you plan on having a heavy load on your Minecraft servers.
Absolutely not.
SSDs aren't all that necessary for Minecraft servers. As long as your HDD can perform you should be fine. I'd recommend using enterprise drives if possible. A normal HDD will struggle to keep up when several players are rendering new chunks. I would entertain the SSD idea, but if you're going to have a lot of players then that world file will get pretty big pretty fast, and we all know what happens to SSD prices when you want more capacity.
Oh dear. Um...yeah...I'm not too sure about that. For your criteria you're going to need a respectable dedicated machine. $250 just wont cut it, unfortunately. A small form factor is achievable. Maybe consider buying second hand 1U servers? That might be a good place to start.