Some ideas:
1. Join a syndicate on angel list
2. Find a private equity guy in NY who can give me exposure
3. Directly invest into friends companies
What are the most recommended ways to get into investing?
AngelList syndicates mostly exist to con rich shmucks out of their money. There are many people with money who long for the prestige of successful Angel investing and will try to take any shortcut available to them, and thus, syndicates have become a great way to capture that free money. Audit some AngelList syndicates for actual success within the syndicate and you'll discover almost all of them are trading off of some tenuous pre-syndicate success (if any at all). Running a syndicate has become its own little industry, often you'll see people joining other's syndicates just so that they'll return the favour to lend some air of credibility.
Likewise, a "private equity guy" will probably treat you as dumb money and just introduce you to his friends who need money and you'll become their new piggy bank until you're run dry. Syndicates and "private equity guy[s]" are basically just crowdfunding for rich people who want someone to fleece them with a personal touch. Finance people who don't have technology experience are a goldmine for hucksters because they don't have the expertise to call bullshit.
Smart money understands that there's a lot of money sloshing around (even in a recession) and that the people most capable of using your money probably don't need it and thus the easier it is to give someone your money, the less likely they are to provide a return.
That's why these "easy" methods of angel investing fall flat in almost all cases: getting in as an early investor in the companies with the best prospects is hard, there's so many people who want to be involved, and founders are choosing the right investors for them... based on more than just money.
You don't need a big network to succeed with Angel investing, rather, you need to have a good network. If you have finance expertise, you should be looking for investment opportunities where you can leverage that expertise.
So, in conclusion, of the 3 options you've presented, investing into friends companies would be the best... and if you don't have a good network of friends building companies that you believe in, then expand your network first, build relationships that are not based around treating you as a wallet and then grab opportunities to invest where you find them. Don't go to "angel investor" networking events, don't try to find a shortcut, don't become a mark.
You need money to be an angel investor, that's the entry fee, but the biggest investment you have to make to succeed is with your time. Giving money away is easy, finding the right people to give it to is hard. If all you want to do is invest money with little effort, stick to the public markets. If all you want is the prestige of being an angel investor, join a few syndicates (but expect to lose your money). And finally, if none of that works for you, I'll take your money!