Nice thread! I started out repairing old gear (kind of necessary when you like old synths) then moved in to more DiY stuff and I've done a handful of things at this point. I'm in no way an expert but here's some advice based on my experience:
Don't skimp on the iron. Get a station with variable heat control. I have a Hakko FX-888.
Learn how to clean and tin your tips (watch videos on youtube).
Don't skimp on solder. I bought a lb of Kester 44 Rosin Core Solder 63/37 for my last project and it made a huge difference in the quality of joints. I much prefer it to lead-free. I just make sure to wash my hands before I eat
Get a flux pen.
Desoldering sucks. Use the measure twice, cut once method and make sure your components are correct before you solder them on.
Take breaks if you get bored or strained. If you solder something wrong it can set you back big time.
You may not need it at first for simple projects but a good meter can be very helpful for calibrating components and diagnosing problems when things go wrong. I have a low-end fluke meter and it's more than I could ever need.
That's excellent advice. If I were to suggest one more thing, it would be to take an electronics class; at some point anyway. It's one thing to poke around and do the exploratory DIY thing and its another to really know what you're really looking at. The knowledge you'll gain will be exponential which will allow you to do larger projects efficiently and safely.