It's not at all disorderly. It's different, but in fact it's pretty straightforward. Thousands of people go through the airport every day with little trouble.

Simply buy a visa sticker at one of the bank windows immediately before going through immigration.
After immigration someone's going to ask to see your passport, so keep it handy.
Go down to the luggage carousels, pick up any bags and off you go.
On the way, one of the limo companies might ask if you want transport: up to you if you want to negotiate here or landside.
You might have to put your bags through an Xray thing in the customs area, but that shouldn't phase you.
Once you are landside stop at the limo desk and arrange transport. Best ignore, or refuse, offers of rides from any touts who have made it into the airport.