Is there a distribution of elementary OS that I can use for installation on a Surface Pro 3 with full support for touchpad and Wi-Fi?
As @Suici recommended, you should try to run it from the USB to see if your hardware is compatible (out-of-the-box, anyway). If you're unfamiliar with the procedure, when booting from the installation USB of elementary, you can choose to either install it right away, or try it. If you choose to try it, elementary will run full-blown operating system from the USB, and at that moment you can see what works and what doesn't.
It will probably work, since Linux has great hardware support, the only thing that may not work is the touchscreen, but I may be wrong (I never tried installing to a touchscreen device).
I have Elementary 0.4.1 on my Surface Pro 3. Basic features all work well, and support has even been added for trackpad scrolling gestures.
I have had problems with the wifi dropping after a few minutes of use when using my university network; however, using my home network does not cause this problem. One other limitation is that the power button will put the surface to sleep, but then it has trouble recovering. After being put to sleep, the surface has trouble recognizing the keyboard and often just requires a full restart.
Overall though, decent experience. Elementary looks great.