When it comes to making music on cheap gear, here's what I've got for you:
Tip #1: Replace the stock hardware.
The most expensive guitar that I own cost about $450 new. That said, I did pimp it out as soon as I could afford to. With nearly all of my guitars (which isn't very many), I have replaced the pickups and the tuners, and in some cases, the switches and potentiometers (volume and tone). Control the variables that you can, such that the music can then flow without hindrance.
The way I see it, the most important thing is to have an instrument that stays in tune. If it doesn't, then it really doesn't matter how well you play it, because it will always sound like an instrument that only produces sour notes, mocking even the most meager attempts at virtuosity. Even Moonlight Sonata would sound something akin to stray cats getting funky.
After the tuners, the second most important thing is replacing the pickups, as that can make a huge difference in shaping the overall sound. Stock pickups usually suck, and using a soldering iron isn't very difficult. Just don't breathe in the fumes when you're doing it and be sure to unplug it when you're done. (That's the dad in me talking.) I'm sure there are videos out there to walk you through the process.
I paid $220 for my Telecaster, used. That was about four or five years ago. It's Mexican-made, as are most of my Fenders. The thing is, when you switch out the electronics, all of a sudden a relatively cheap guitar sounds like one that cost a lot more. Seriously. I think the cost-to-quality ratio plateaus at a certain point when it comes to guitars.
That is to say that a $300 guitar may indeed be twice as good as a $150 instrument, but never in my life have I played a $2,100 guitar that sounded seven times better than the $300 one. I have, however, played a $300 instrument only needed a few modifications to make it sound just as good as one that cost five times as much. In fact, I play an instrument like that every day.
Tip #2: Thicker strings will make your pickups sound better.
I have found that I can get a much fuller and richer sound if I use thicker strings. They also stay in tune better, because they don't stretch as much under the tension. Personally, I always pull on the strings after I put them all on, just to try to get some of that initial stretch out of the way. It's also a good way to make sure everything is secure before you start tightening it down.
Thicker strings will toughen up your fingers, too. They may not be the best for beginners, but once you've got decent calluses and finger strength, consider upgrading. You might be surprised how much bigger it sounds. Much like replacing your pickups, thicker strings give your amp and your effects pedals more defined vibrations/signals to work with, which is usually a good thing.
I should note, though, that if you are changing to heavier gauge strings, it can affect the action, since it's putting more tension on the neck. To accommodate for this, you can adjust your truss rod. Again, you might want to watch a video to feel more comfortable with what you're doing. The basic rule is: don't turn it too far too fast, and I highly recommend doing it when the strings are off the guitar. Let the neck ease into the adjustments by doing them in increments of about a quarter turn. If it's still not quite right when you string it back up, you can always make some more adjustments next time you change the strings.
Tip #3: Stop buying new bass strings.
If you happen to play bass, you know that the strings are kind of expensive. They also hardly ever break, and if they do, then congratulations, you may already be a punk rocker. Breaking bass strings is hardcore.
A long time ago, a good friend of mine told me that if you take the strings off and put them in a pot of boiling water for a few minutes and then put them back on, they will be as good as new. This really does work. I have gone years without actually changing the strings on my bass just by boiling them every once in a while. Just make sure they're dry before you put them back on. Water and frat dudes are a string instrument's worst enemies.
Tip #4: Clean your guitar strings and you won't have to change them as often.
I'm happy to report that there's a similar trick when it comes to guitar strings. Although taking them off and putting them back on is nearly impossible (and would probably weaken them considerably even if you could), what I usually do is take a paper towel, fold it up and spray it with a little bit of WD-40, and then I put the towel under the strings so that the oily side is facing up. I'll go up and down the strings a few times, and it never ceases to amaze me the amount of crud this takes off, a nasty combination of corrosion and finger gunk (and it's not like my hands are dirty when I play, either). Generally speaking, the more humid it is, the more often I have to do this.
I should offer the disclaimer that I have never heard or read of anyone recommending the WD-40 method before, but I can attest that I do this on my guitars on a pretty regular basis and have never had any problems. If anything, I think that the oil actually helps seal the wood on the fretboard (the WD does stand for water deterrent, after all).
Then again, as mentioned above, it's not like I'm playing a $2,000 guitar or anything. I wouldn't recommend doing this on coated strings, either, because it would probably take the coating off -- but I have been doing this for years, such that most of the time when I change strings, it's only because I broke one of them (which doesn't happen as often now that I use thicker strings). Clean them up every week or two and they continually sound almost as good as new.
Tip #5: Learn the lighter trick.
As long as you're fixing to be a punk rocker, at some point, it might be a good idea to learn how to open a beer bottle with a disposable lighter, too. Otherwise, I'm not sure that you can actually call yourself a punk. It's one of those technicalities. As for how to do it, it's essentially about creating a lever with the lighter by using your bent thumb as the fulcrum. Then you pop it off with the bottom edge of the lighter. Oh, and try not to crack it in the process, especically if it's someone else's lighter. You lose a few punk points for that.
Tip #6: Treat your instruments well.
One last tip for today, which I admit is slightly less punk, though more closely related to maintaining decent instruments: if you want to clean up the fretboard, use 0000 grade steel wool (I'm pretty sure that's the "softest" that you can get). Once you've scuffed up the whole fretboard, wipe it down with a damp towel, but then dry it immediately afterward.
Always remember that one of the worst things for a guitar is for there to be any absorbable water on the fretboard, as this will warp it, rendering the instrument utterly useless. Second to this, as alluded to earlier, is to let it fall into the hands of someone who intends to use this instrument for evil purposes, like Jimmy Buffett songs.
When it's completely dry, rub it down with some lemon oil. Wipe away any excess. It might even look like brand new when you're done. You'd be amazed. Granted, like I said, I don't know how punk rock it is to have a clean, new-looking instrument, but personally, this is something I do to my guitars about once a year or so. It probably helps to take off any remaining residue from the WD-40, too.