I've just been sorta tooling around for a couple years on a $250 acoustic guitar. I've switched between light and medium strings and didn't notice much of a different feel, maybe a bit of a different sound but I wasn't paying much attention at the time. I understand the theoretic difference, and since I'm not much of a Bendy McNotePlayer, and my bass-trombone upbringing fills me with a desire to rattle windows and frighten children, I think I'll like heavier strings.
Anyways...do I like...need to do things with my action? And truss rod? I always thought those kind of adjustments were more of an electric guitar kinda thing and I never paid that any mind, I wasn't even sure I could do all that on mine. I'm actually still not sure, google confuses me. Is it one of those things that I'm probably not good enough to care about? I feel woefully un-learned when it comes to my guitar.
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The answer is probably gonna depend on how well your guitar has been set up now and how much you play up the neck. If its been properly set up and you switch the strings over you'll notice it starts to go out of tune on the higher frets. You might be able to learn how to intone it and knowing how to set up your own guitar is a very good skill to have.
On my guitars, if the nut isn't properly cut for the string gauge, I'll throw a fit. That's an adjustment better left to a skilled luthier, and something you probably won't notice or care about. Particularly on a $250 acoustic guitar.
The truss rod might need an 1/8th or 1/4 turn to adjust for the extra tension from the strings. This is not the same as adjusting your action, and don't let anyone trick you into thinking that it's an acceptable substitute for a properly set up nut (as previously mentioned) and bridge, which are the two things which you need to adjust if you want to set up your action.
As romanquerty mentioned, the bridges on acoustic guitars aren't quite as versatile as they are on electrics, but the actual point where the strings touch the bridge (most likely a white plastic bar) can be raised a tiny bit, or changed to help compensate for intonation, again, as romanquerty was mentioning.
I would suggest going ahead with the string change, just to see what it's like. If there's something about the way your guitar plays after the change that you don't like, then come back and post about that specifically.