I have a few notes:
First, According to what I've heard from astro-physicists, we started sending radio signals into space about 60-70 years ago. Signals would take between 5 and 30 minutes to reach Mars, depending on relative positions due to orbit, so once both of us were able to send and recieve, we'd know almost instantly about each other - even assuming we hadn't already figured it out via telescope. Assuming our relative forms of communication were similar enough for translation to be possible - Which is reasonable if we can understand that they ARE communicating, and virtually impossible if we cant - Linguistics shouldn't take too long to do so, even if we have to get by communicating via math.
How we would respond to each other would greatly depend on the above - If we can't communicate with them, then Darwinism kicks in - If we can't know they aren't meaning to destroy us, we will - as a dominating and very self-preservative species - destroy them first.
"If you can't speak to the other guy, you can never be certain he's not trying to kill you."
On the other hand, if we CAN communicate with them, then other possibilities open up - Yes, conflict would be all but inevitable given our history, but it would be very similar to what happened when different societies first encountered each other on Earth.
Now, as to the travel.. The problems with sending stuff into space is Politics. Yes, it's costly, but think about this : The recent Curiosity mission to mars cost 2.5 Billion, from R&D to Launch, sending a nuclear powered mobile science lab across space and landing it safely without any assistance at the other end - and that was far over the estimate due to problems that I won't get into other than to say they wouldn't have happened if there was political motivation to get there.
The United states Dept of Defense spent ~700 Billion just last year. Many current fighter jets cost around 100 Million each. Not counting the few billion they spend on R&D every year. Heck, the B22 spirit bomber.. which they have a couple dozen of.. EACH cost the same as Curiosity. Not counting the bomber's R&D budget.
Now take into account that if there were KNOWN Intelligent life out there, the drive to go out there - whether for trade, war, exploration, whatever - would be so much greater than it currently is. Especially if they're that close. If we found out about them around the 60s, when all the space programs were getting started, we'd probably have had unmanned probes there by the early 70s, and a manned mission by the 80s at the VERY LATEST. It took NASA 8 years to go from 'holy crap the Russians put a guy in space!' to "Hey look, we're on the moon" because there was drive to do so.
Though that's assuming we're more advanced than them and they don't beat us to it.
Consider this; A 5 minute video of thoughts from Astrophysicist, Science Popularizer, and Directer of the Hayden Planetarium - Neil Degrasse Tyson.
It's called 'we stopped dreaming' and combines a lot of his great quotes/thoughts about the american space program. I seriously suggest watching it. It's a bit heavy on the american patriotism, but still very insightful and moving to anybody who's interested in space.
http://www.youtube.com/watch?v=CbIZU8cQWXc
Imagine if instead of the Americans slowing/stopping space exploration, they and all the rest of us had encountered a catalyst to go further - Extraterrestrial Intelligence.
I cannot fathom the concept that we would NOT be capable of travelling between Earth and Mars efficiently and readily by now.