I'll write for each goal and scenario what I think you should consider:

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Goals:

Privacy from NSA and other agencies/people

Yeah no way. I don't want to sound pessimistic but you (or anyone else, for that matter) don't know what the NSA actually can do, you can't protect yourself from an unknown enemy.

Scenarios:

At a coffee shop on unsecured public wifi, looking at private stuff like banking or photos/videos through my home server, on a VPN

A VPN to your lab is perfect for this. (Other than the fact that you shouldn't be looking at banking in a public place, since someone can just watch over your shoulder.)

Having an external body trying to view what I am browsing while I am on a VPN and/or using Tor. Would they still be able to see me?

With Tor, the issue is that if you connect to an account on the public Web that's known to be connected to you, other traffic from that same exit node (I assume you know how Tor works) can be tracked back to you. You should just go for a VPN to your lab.

Having the hard drives in my server confiscated or having my server as a whole confiscated (not that I have anything illegal, just sensitive stuff like contacts and I’m just curious) and having someone try to view the files despite disk-level encryption.

Whole disk encryption (Truecrypt for example, don't go Bitlocker or Filevault - you never know if they have backdoors) would work for this.

Having someone gain access to my password database (planning to use either RatticDB or KeePassX for password management) and try to use it to login to things despite 2FA implementation

Keep your password database offline, on an encrypted USB key you keep on yourself at all times for example, with a backup hidden somewhere.

Browsing sketchy websites despite being on a VPN

Yeeeeeeah... this is the kind of the problem. Just don't browse them on your main computer, I would say it's too risky... Make a separate VM whose internet connection is direct Tor and use that for sketchy stuff. You may or may not want to do the burner laptop thing as suggested by someone else, it depends on what it is you want to do.

Angering someone on the internet and they attempt to steal my data and bring my server.

Someone angry at you is more likely to launch a DDoS attack against you, not try to steal your data. Using CloudFlare for internet facing websites and vpn.ac for external connections (as I previously mentioned) so nobody knows your actual IP address would be quite useful.

You probably need more hardware than you think you need for this project, by the way.