If I upgrade to 2G of RAM, it looks like I can upgrade to Lion, but not Mountain Lion. I was going to upgrade the RAM anyway because it seems to run a bit sluggish, but the Mini maxes out at 2G, which is the lower limit of Lion. So it may be a wash, performance-wise.
No, it will be a huge step backwards. Do not, under any circumstance, install Lion if you can possibly avoid it. Not only is 2GB not enough to run Lion in any reasonable manner, but even if you have more RAM than that, Lion is a molasses sucking pig. The last OS for any hardware I used that was that bad and that much of a step backwards from what came before it was... umm... Wow, can't think of one. Lion wins. Or, actually, loses.
Installing it was the worst single decision I've made regarding Apple software on my early 2008 MacBook Pro. I even did a clean install from official Apple USB media (i.e. the USB fob you had to pay extra for instead of just downloading it) and upgraded RAM to 4GB on account of Lion. Take it from myself and several of my coworkers who regretted every getting within 100 feet of Lion that it is best avoided. Mountain Lion didn't suck, but only by comparison to Lion. Mavericks is a little bit better yet, but still not nearly as snappy as Snow Leopard.
My gut reaction: Don't worry about Snow Leopard being out of date, even security-wise. A man-in-the-middle is rare in most environments, and Snow Leopard is already quickly diminishing in market share, so it's not terribly likely to be widely exploited. Compared to the every day pain you'll cause yourself by installing Lion or later, the tiny risk profile of running a vulnerable Snow Leopard is worth it, in my opinion.