Mountain Lion is a little more taxing than Snow Leopard on the older Mac's. However it should run OK on your Mid 2007 iMac, if you have plenty of Free Space and upgrade the RAM from 2 to 4 or even 6GB.
check out > OWC iMac Memory
As den.thed has pointed out, if you're looking at running Mountain Lion on your iMac, you'll want to max out your RAM first. The total cost for that will be well under $100. He's right in that Mountain Lion is a bit more taxing on your system than is Snow Leopard. But...the additional load it places on your hardware may be mostly made up by the additional RAM.
I think it depends on what new features only available in Mountain Lion you need? You mention AirDrop, but I don't think your iMac supports it, since it's hardware as well as software dependent.
Here's a link to the computers supported by AirDrop. Unfortunately, yours isn't supported.
I hope this helps.
If you wanted all the new features of the newer Mac's and the newest version of Mac OS X then maybe you should of bought a NEWER Mac. The one you have is now going on 6 years old. It may not even qualify for installing the newer version of OS X, To Old.
Just use it as is and if you don't get on with OS X and the Apple/Mac way of doing things you can sell it for close to what you paid for it and buy something NEW that you are use to.
Your machine needs to meet these to run Lion: http://support.apple.com/kb/SP629. Since you're new to Macs, learn to use what you have before embarking on upgrading, especially if your machine doesn't qualify. See these, ignoring anything related to windows if you're not familiar with it:
Additionally, *Texas Mac Man* recommends:
I have a 2007 2.4Ghz Intel Core 2 Duo with 4 GB 667 MHz DDR2 SDRAM and I am running OSX 10.8.2. To work around the AirPlay I use AirParrot ($10) that works fine with my Apple TV. I have not played with newer models to know the difference, but mine is quick enough for me to process home movies.
But as stated above make sure yours is compatible.