I have a wiki currently, which is easily accessible and updateable from anywhere by web. Is that something that org-mode can provide, or do I need to ssh into a machine (ie, harder from a mobile device)?

There are some apps but I found that sshing to another machine was the best solution. An alternative is to run Emacs locally.

Absolutely agree - I've got most of my stuff hosted such that I just need SSH (or a VPN) to access it. However, usability on a mobile device in this case is limited (albeit not impossible).

Usability is not a great problem if the phone has a big display (5.5>) and you use evil(vim)/evil-leader for your keybindings. JuiceSSH and mosh also help with latency and disconnections.

The main problems for me are:

    1) Keeping everything synced. Especially Emacs's state. 
    2) I don't trust a VPS with all my personal information.  I have *everything* in org-mode files.

The first problem can easily be solved by using a tmux session that is shared between smartphone and laptop. The drawbacks would be that I can't access said session without Internet and also that I lose emacs's gui features like the pdf-reader. x2go is fast enough but they don't have an android client. I have yet to try nomachine.

Org mode can easily generate a static site from all your content. I've never tried remote updating, but Org mode data is all just simple text files, so you could just use Dropbox or whatever.

There are mobile frontends available:

http://orgmode.org/manual/MobileOrg.html