Ilya,
Just purchased our first property and it was quite uncomplicated. As stated by ecarigan, you do not have to be physically present for closing, your RE agent can do that for you if they have residency (and if they are trustworthy).
We wired the money to our atty's escrow account. Should be no problem if you use a well recommended attorney.
Best of luck to you. We make our first visit to our North Coast hideaway soon.
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