Should I start angel investing?
So the first thing I always tell people is venture investing is a very easy way to lose a lot of money. Most startups fail and never even return the full amount invested in them. The earlier you go, the more risk. The last few years have seen a massive rise in secondary markets that you could buy into, and valuations are quite a bit down from the go go period of 2019–2021. I guess the same is true for public markets.
Given all this, only invest money you are ok with it going to zero. The best way to get started is to invest in your network — people you know or people they know starting companies who want to give you a chance to invest. You can try angelist or republic or other paths like that, but i think those tend to have some adverse selection. My general advice to people in tech is invest your money in safer broader things, until you really have enough you are willing to just lose it
Should I work at a VC firm to learn about startups and investing? What if I like building?
A job at a VC firm should never be the first time you are visiting startups or hanging out in their offices. Do the work ahead of time. Get to know friends with startups, visit them in evenings, jump on weekend phone calls, jam, help if they need it. An entry level VC role is usually not recommended, but it can be fun if you are already doing all of this as a hobby (I sure was!).
But be warned, it is very much not building. Based on your (3), i would say the most fun you can have is having a great building job and occasionally advising or angel investing in companies on the side. This way you still build as your core day job, but enjoy the side hustle of getting to help startups. For me — I spent 15 years at startups (LinkedIn Facebook twitter when they were all much smaller) before becoming a full time VC. I did that for 7 years but I missed building so returned to operating about 5 years ago.