I use RealVNC 5.3 free version on my Macs to access a RealVNC server (also the free version) on a Windows 7 Pro machine in the office. Fast on my 7.5Mbs DSL link, low overhead, scalable window, and just works great. I find it better than MS RDC because I don’t have to log out of my Win7 machine which runs scheduled apps at night. RDC logs me out and the apps don’t run after I disconnect. Google’s Remote Desktop is another good one too… if you don’t mind Chrome sitting idle in the background.
Edit: I just checked… sorry, no iOS version of RealVNC yet. macOS, Windows, Linux, Pi, Solaris, and AIX clients available.