Easy to be overwhelmed. It'll start to make sense, just look for the common information that you'll keep hearing from trusted sources.
"People say go with index funds (but don't really specify which one)" -- Yes, this is the first key. You want a specific one: VTSAX for your taxable investment account. I also like 10% of my total investments in VBILX (intermediate bond fund), and 10% in VGSLX (REIT Index). The latter two are part of my IRAs, which makes the taxes easier. Mmost of my investment $ is in the taxable account in VTSAX. My IRAs are a mix of VTSAX, VGSLX, and VBILX. The overall total percentages are approx. 80/10/10, which is somewhat aggressive.)
"others say invest in dividends and compounding interest is great" -- Many stocks pay dividends. If you're in a stock index fund, like VTSAX, you're getting dividends. Your bonds are earning interest. You can't really 'invest in dividends,' but dividends are one way that stock funds grow. Follow the above advice and you're investing in dividends and getting compounding interest.
"others say you should do active trading" -- The only people who say that are people who profit from your trading. This is the number two biggest mistake you can make (the number one mistake is to stay overwhelmed and not invest at all). Lots of research shows that most stock professionals cannot even regularly match the market, much less beat the index funds. The typical home investor will be destroyed by active trading.
"buy only when market goes down" -- This is known as market timing, and since you cannot predict when the market will go down, you have to sit on your money waiting, while the market is going up. Then, when it goes down, how do you know if it's really hit bottom? The best strategy is to invest as much as you safely can, as often as you can, as soon as you can. If the market goes down, and you happen to have some extra cash, by all means put it in the market. But I've known people who have been waiting since 2011 for the market to go down, and they've missed a tremendous appreciation in the market. If you worried you'll invest and immediately the market will go down, then invest in several chunks over the next 6 months. But you should be taking a long-term approach, not trying to maximize short-term gains.
"others say gold is the best" -- Gold is a terrible investment. Period. But the 'goldbugs' are an active, loud little group on the internet. They are also wrong. Look at the history of gold prices over the last 40 years. It's ugly.
"max your Roth IRA" -- If you're in a fairly high tax bracket, traditional IRA is better (Uncle Sam essentially contributes $1500 each year to my traditional IRA). But either way, yes, max your IRA out, whether you choose traditional or Roth.
"but be careful they might change tax laws" -- sure, they might, but they're never going to take your money away. Invest as much as you can now, and worry about tax laws when they change.
"max your 401k" -- Yes!. If you have access to a 401(k), which has much higher limits than an IRA, definitely max it out (you only get access to a 401(k) through your employer, and not all jobs offer a 401k). Even crummy 401(k)s are good, and you should be able to find a couple of funds that work for you. Don't fall into the trap of ignoring the good because it's not the best possible. And if you have a 401(k) and then change jobs, roll that 401(k) over to Vanguard in a Rollover IRA, and get those lower fees working for you.
"but I can't touch" -- there are strict limits on taking money early out of an IRA or 401(k), but there are situation when you can without penalty. In any event, your IRA/401k should not be all your investments. You should also have a taxable investment account, and an emergency fund. The tax benefits of 401k/IRA easily outpace the restrictions.
"but I think I've got crappy funds" - crappy funds are better than no funds. The tax benefits are awesome. Just keep it simple, and don't stress over it. I only wish my job offered a 401k with crappy funds.
"from my age, I see less job security, shorter working career, higher costs of living in my generation and the future looks pretty difficult in terms of living and achieving goals+stability." I don't know why you think the cost of living is going up. Inflation has been super low (in my youth it approached 20%), and I currently pay the same for clothing as I did 30 years ago, for example. You may have a shorter working career, you may not, who knows. In any event, unless you plan to live a short life, you should invest for the long run, which means putting the majority of your investments into stocks, and understanding that there will be ups and downs.
"People also mention a correction is coming and a chance for 2015-16 to be bad years" -- Look around the internet. You can find solid, well written articles saying 2011 would be terrible, or that a correction was likely inn 2012, or 2013, and then surely disaster would hit in 2014. 2015 or 2016 may be bad. They may not. The market might drop 25%, and then 9 months later be slightly up for the year. You can't control that. You CAN control saving lots, and building an emergency fund, and fully funding your 401k or IRA, and building your long term investments.
"Just looking at the table and news and stories of people around me, it feels like economy is really bad" -- Same as it ever was. MMM has talked often about how much better life is when you're optimistic and mostly ignore the news. He's right. Or you can read the news from 5 years ago, and 10, and 20 and 60 years ago, and see that there are always bad signs around the corner, and the economy seems to be faltering, and on and on.
"I have to worry about learning how to invest and all the different things to out look for, it's like another job." -- Reread the first thing I wrote above. You'll see very similar advice from Jim Collins and MMM and John Bogel and William Bernstein (wonderful writer about investing) and others. Subtle details may change, but in the long run it's probably minutia. You're making this more stressful than it needs to be. If you're really risk averse, change the 80/10/10 percentages I recommend to 60% VTSAX and 30% bond index fund and 10% VGSLX. Just be sure to rebalance once a year or so. Or just invest in a target retirement account and never check it. Start shoving that money into Vanguard accounts, then try to forget about it. Stop listening to anyone talking about the economy on TV, keep saving like crazy, and I promise you that when you look back in 6 or 8 years you'll start to feel really good about this stuff.