Rational or not i think reali depends on whether wat you want
outta it and where you stand. I think you have a realistic,
reasonable and healthy outlook if you really only want to know her
better and do not expect to get anything out of it. yes, you will
never know if you 2 can click until you start hanging out
together.
Afew thousands may not be alot, but could be a fortune to some. So
it really depends on whether what it is to you. One thing to
caution you, if you buy her the air ticket now, it may set the pace
of the relationship.
Lastly, i think webcam is a good idea. Also, you can start with
skype 
