My DS was adopted from Korea almost a year and a half ago and we are in the middle of the homestudy process for #2 from Korea right now. I can't begin to say enough wonderful things about the Korea program FOR US. Every agency and program is different - if you do your research you will find the perfect program FOR YOU!
I know this stage in the process can be incredibly overwhelming. The absolute best thing to do right now is to get real, hard, cold facts about the options in your area. There is SO much misinformation (and sometimes hurtful info) out there, so make sure you're working with facts and not myths.
In my mind, the single most important decision we made was choosing our (fabulous, fantastic, amazing!) adoption agency. (In case you're in the DC area, we used The Barker Foundation.) Working with an agency (or county Department of Social Services) that you trust makes the process so much more smooth. There are a lot of fabulous agencies out there, but unfortunately there are some snake-oil-salesmen as well, so make sure you are dealing with an agency that is trustworthy, ethical, and respectful of all three sides of the adoption triade (kids, birthparents, and adoptive parents).
Talk to your county's foster care office (Department of Social Services, or whatever it's called where you are.) In our county, there is no "foster-adopt" program, so you have to be willing to be a foster parent. A lot of counties do place for adoption through the foster care system, though - you just need to get the info from your own locality or find an agency willing to do out of county placements. Assuming you aren't working through the foster system, get a list of the approved agencies in your state - a quick internet search should find your licensed agencies in your state. Some are national and some are local. Read about them online, call or email them for their info packets, go in person to their info sessions (we didn't use one very respectable, perfectly legit and ethical agency because we just didn't feel comfortable at their info session - talking to the people in person is HUGE!)
Many agencies have multiple programs. In our case, we initially had chosen domestic adoption, but chose to switch to Korea after a few months. Fortunately, our agency has both programs, so it wasn't a big deal. Just another thing to consider when choosing agencies.
With your ages, assuming you have no major health issues, you should be able to choose pretty much any program, so just do your research and follow your instincts. With our agency, your youngest child has to be 18 months when you start the process, so you're definitely in the right timeframe.
If you have any questions about the Korea program (or anything else) please feel free to PM me or just post it here.
Good luck!