What are the best practices regarding personal files and encryption?

Some background info for understanding full-disk encryption - think of everything in terms of layers. At the bottom layer (for our purposes) is your SSD or hard drive. In Linux terms it's a block device. It has small, fixed size blocks (512 bytes, or 4KB on some newer drives) and each block gets a number. You can ask "write these 512 bytes to sector #1234" or "what's stored at sector #1234" but that's about it. At this layer there's no concept of files, filenames, directories, etc.

Layered on top of the block device is part of the OS called the filesystem. You ask the filesystem "what's stored in the /home/kfwyre/Documents/ directory?" and it knows what blocks of the disk to go read to look the directory listing, including filenames, sizes, modification times, and all that. And for each of those documents, it knows what blocks of the disk they're actually stored at. For 100-byte files it'll know that only uses up a partial block, so it reads all 512 bytes but ignores the extra 412 bytes^[1]. For a large file, it knows it needs to split it into multiple blocks, so it'll allocate a single span of "block #1000 to #2000", or it'll store a list of "blocks 1234, 3456, 7890..."^[2].

^{1: If the filesystem is smart, and modern filesystems are very smart, it won't actually waste those 412 bytes, but cram another small file in there, or cram the file's metadata in alongside the contents itself, or something along those lines.}

^{2: If you're old enough to remember the good ol' days when your computer would get slow and you'd defragment your hard drive and it'd get faster, this is what was happening under the covers. You'd have a file scattered across your hard drive, and reading that file would send the filesystem on a wild goose chase all over the actual disk. Defrag would take the blocks of the file and move them into one long contiguous segment on the disk.}

The full disk encryption I'm talking about (LUKS) is yet another layer. It gets sandwiched so it's sitting on top of the disk block device, but below the filesystem, and it acts like just another block device.

So the filesystem says "here, write this data to sector #1234", and the data the filesystem is working with is unencrypted. Normally that'd go straight to the disk, but because LUKS is sitting in the way, it encrypts the data then writes that encrypted data to sector #1234 of the actual hard drive. Likewise, when the filesystem asks for sector #1234 to be read, LUKS reads the encrypted data off the disk, decrypts it, then hands the decrypted data up to the filesystem.

This is why you'd need to wipe+reinstall to start using FDE - right now all your data is sitting on the disk unencrypted, and the moment you put that LUKS layer in, it'll expect everything to be encrypted.

For your questions about whether apps like Syncthing and Spideroak will deal with encrypted data - nope, they won't. They're layers on top of the filesystem.

What will happen, is say you've got Syncthing running on two machines, both with FDE. Syncthing reads the file from one machine, which goes through LUKS to decrypt it, then it sends it over the network to the other machine. That connection is encrypted by Syncthing, so someone eavesdropping to their conversation wouldn't be able to get your file. Then the other machine takes the file, writes it to disk, which goes through LUKS to encrypt it on-disk. The two machines will be using different encryption keys (even if they have the same FDE passphrase) so if I stole both of those disks, I wouldn't even be able to tell they have the same file on them.

Similarly, Spideroak reads a file from your disk, LUKS decrypts it as it goes, then Spideroak encrypts it with a different encryption key and uploads it to their servers. If your home is hit by a meteor and you have to recover from your Spideroak backups, it's OK that your encrypted drive was destroyed, because you just need your Spideroak credentials and you can download your backed up files, unencrypted (though if your new machine also has FDE, they get encrypted the moment they're written to that new disk).

This also answers your question here:

if I encrypt my disk and then look at it without the encryption, would I still see the same directory structure and number of files in each folder but just with encrypted names and filetypes, or would it just be just a large unrecognizable single chunk of data?

Full disk encryption means everything is encrypted, even directory listings, filenames, etc. This is because the filesystem layer has to write a block to disk saying "here's the contents of the /home/kfwyre/Documents directory" and since that goes through LUKS too, it gets encrypted like everything else. If you went block-by-block over your encrypted drive, you'd have a small unencrypted segment at the beginning, containing your /boot partition - the bare minimum Linux needs to start up and show you an enter disk encryption passphrase: prompt. The rest of the drive would be absolute gibberish, indistinguishable from random noise.

As far as performance goes, it shouldn't be noticeable, even for gaming. The reason is that as fast as SSDs have gotten, CPUs are still faster, and they have special instructions that accelerate AES, the encryption algorithm used for this. On my desktop (a ~4 year old Haswell i5):

$ cryptsetup benchmark
...
        aes-xts   256b  2094.6 MiB/s  2094.8 MiB/s

There's other algorithms listed in the benchmark, but that's the algorithm I'm using, and the default if you were to set this up. My 4-year-old CPU can encrypt and decrypt data at 2 GB/sec. My SSD isn't anywhere close to that fast, so reading data off the disk isn't slowed down at all by the encryption (though it might increase my CPU usage by 1-2%).