How you connect to a system, in terms of target IP address and authentication mechanism, is defined by the server - not the client. In this case, the server is your work computer.
Unless there are specific firewall rules applied at some point between the client and the server, the client device's IP does not matter. It is very unlikely that you will need to keep track of, or make special accommodations for, IP changes on your home system in order to connect to your work system. The only IP you will need to keep track of is that of your work computer.
Regarding network access to the work computer, you do need to know whether that computer's IP is static or dynamic (and, if it's dynamic, whether you can find the computer by its DNS hostname) and if there are any special requirements to connect to the system from off-site. Most business workstations are not publicly accessible without connecting to the corporate VPN - you should check with your company's IT department to see if they support VPN connections from Windows 8 systems.
Your home computer also has practically zero effect on how the authentication process takes place. When you connect to your work computer, and are prompted for credentials, you will need to provide the username and password (and/or any alternative two-factor mechanisms required) for an authorized account on your work computer or its domain. Usually, such accounts are entirely endemic to the local computer or domain - you will not usually be allowed to log into your work computer with an account of your own choosing or creation, let alone with your Microsoft account.
What you really need to do, to find out how to properly get remote access to your work computer, is contact your company's IT department. They should have all the answers you need - and, if the answer is just "no", you need to stop right there.
I am a sole business owner. I sublease from another small business. I have access to their router login/pw. They use FIOS as well, although it may be static since it is a business account (will have to check if they got that package). In other words, there is no IT department. :) Thanks for the detailed answer. – REMESQ – 2014-09-04T13:24:46.527
@REMESQ In absence of an IT department on the business side, check with the ISP regarding whether your IP is static or not, and you should coordinate with whomever shares the router to make sure the port forwarding rules you'll need don't conflict with their requirements. If your Internet-facing IP is indeed dynamic, you can use a Dynamic DNS service (Dyn used to have a free edition, but I think it's all paid now - others may still be free.) to help keep track of it...
– Iszi – 2014-09-04T14:48:20.360...However, you should not generally expose RDP to the Internet like this. Access should be restricted by VPN and/or other mechanisms. – Iszi – 2014-09-04T14:49:19.910