Which edition of Home? Is it Home Basic or Home Premium?
Personally, I would take the laptop with the better specs. You can always install a better version of Windows later. Plus with the better specs your performance will be that much better.
As for installation... it is my understanding that you can always upgrade from one version to another one "higher" than it, but I recommend doing a clean install. In either case, you can always upgrade.
Define "remote access". Do you mean simply Remote Desktop, or something else? I'm pretty sure Home Premium can do what you'll need it to do. Perhaps try asking at the IT department at your work.
EDIT: here's a comparison chart for the different Windows 7 editions.
http://en.wikipedia.org/wiki/Windows_7_editions#Comparison_chart