I didn't say one card would absolutely do that (although a rejection - which is not unusual - can hurt). You said you were thinking about opening - and then closing - ten credit cards. Your credit could be badly damaged (for years) before you got half-way through that.

Again: nobody is going to do the work for you. Don't be lazy. Why 2? Is that a magic number? Why not one, or three?

The answer to your question is it depends. There is no perfect, correct answer for everyone. The answer for me (someone with good credit good income, a long established relationship with all the banks, 20+ credit cards already, and a bunch of other factors) is going to be very different than it is for you. Or the next guy. There is no one size fits all.

You speak in sweeping generalizations of your goals:
Get out a map. "Asia" is a big place. Japan, India, Mongolia, Signapore - they are not all the same. Do you have an actual destination in mind (if so, what is it? the details may matter), or do you just want to see yourself in one of the pretty pictures the bloggers post?

The point is that in your case - someone completely new to all this, with (as you say) low income - and thus probably very limited ability to open large numbers of credit cards - and (to be blunt) not much of a grasp of how it all works - you are going to need to be careful, you are going to need to stay focused, and you are going to need to make smart choices, if you expect to succeed. Lots of people don't.

txflyer77 makes some excellent points. How many people are you trying to get to "Asia"? Just yourself? (in that case, it's less difficult). Got a spouse and or kids you want to bring along? It gets a lot harder as the number of seats you want increases. How flexible are your travel dates? No flexibility (eg school vacations, major holidays, etc.) means things get much, much harder. It's easiest if you have no job and no responsibilities, and can go by yourself with zero notice - a seat suddenly opens up to Jakarta in 3 days, and boom, you can go - great. But that's not how most of us travel. These factors are not trivial - they will make or break your efforts. One person who can go on any day is completely, utterly different from you+a spouse+a kid or two constrained to specific travel dates.

Pick a specific destination (or better yet, have a list - 'cause that flexibility thing is always working against you). Then learn about which airlines can most easily get you where you want to go. Figure out how many seats you need, and when you would like to use them.

Here's the dirty little secret the bloggers tend to ignore: getting the points....that's the EASY part. Actually using them - without paying double or triple the points - is actually the hard (often impossible) part. Most people only figure this out after they have some points and go to try and use them - then they conclude that the whole thing was a waste of their time.

Figure out where you want to go, when, and how many of you there will be. Then go try doing a dummy booking for that. Look for the ways that you could get to a few of your top priority destinations - use travel dates that are realistic (ie if you can't just drop everything and fly to Bora Bora alone on Thursday because a seat opens up, and instead you need to go during Spring Break with 3 others, be honest with yourself). Then do the math. How many points you gonna need, in whose program. Then figure out how long and how easy or hard it would be to get those points. Don't forget to allow for program devaluations, which happen with increasing frequency (figure once every 12-18 months to be safe).

This is not a game for those who can not or will not learn, for those who are not good about tracking details and following up.

Do your homework. That's the only way to know what strategy is right for you. If it's too much trouble, then sure, I have a credit card recommendation: just get any Capital One card*. They have cute commercials, and whenever I hear someone demand to know what's in my wallet, I feel intimidated, so I just apply for one of their cards and hope for the best.

*sarcasm - not actual advice