Yes, it sounds as if you will be better covered with Pro. Most of those functions can be handled with Home Premium, but for XP emulation and the remote desktop function you need Pro.
There are workarounds (I use a different. free package to provide remote desktop) but the effort to set that up may make Pro a more efficient solution in your environment.
Memory - unless you are running very large spreadsheets or apps, 4GB should be more than enough memory.
The graphics card may be a consideration: my laptop does an excellent job except for high-definition videos and video-conferencing causing the thing to get too hot. I had to install a fan-control app to turn up the blower at times. More research into video performance and cooling would have been a good idea.