A few things to keep in mind.  First, now all applications have a maximized state.  You can set the shortcut for calculator to maximized all day long and it will never launch full-screen.  If your application does not have the maximized button in the upper right-corner next in between the minimize and close buttons, it will never maximize.  Second, some applications change their size to a "default" on start.  For those, although Windows may start them maximized, the application itself may resize itself either before you see it, or moments thereafter.

To start with, your router is serving two purposes, first as a DHCP server and second as a low-security firewall of sorts.  In order to allow more than one computer or wireless device to talk not only to each other but use the internet, each unit must have a unique "address".  Your ISP only provides you with one, so when you connect your router to your cable modem, it is your router that gets your ISP's address.  As all units connecting to the router will also need unique addresses, your router in turn provides them with an address from a pool of addresses it is authorized to give out.  This is most likely an address that looks like 192.168.###.### or 10.###.###.###.  I know this because these are special ranges of addresses that anyone can use on any private network not connected to the internet.  This is where your router again comes into play, and it is what is managing a "translation" or "proxy" between your local addresses and the single address that the ISP provided; data does not go directly from your computer to any destination outside of your house, it is passed to your router, your router gets the data and then passes it back to you.

That said, job one for you is to determine what your ISP provided IP address is.  In order to do this, you must connect to your router.  Different vendors have different methods of doing this, but most are thru a web browser where you type in the address of your local computer's gateway.  Determine this by opening up a command prompt and typing ipconfig.  When you see the data, look for the "Default Gateway" address, and use that as the web address (e.g., http://192.168.1.1).  You will most likely be prompted to enter a username and password.  Once you're connected, the next step is to find the IP address.  You will need to refer again to your vendor's documentation to see where they display this, but they all do display it.  Remember this location as you will need to find it again.  Each time your modem / router are rebooted, you may get a new address.

Now that you have the IP address of the router, you need to perform a little more configuration on the router itself.  Because your router also acts like a low-security firewall, much of the non web-based incoming and outgoing traffic is blocked at the router for your protection.  Different applications use different ports to communicate on, and Remote Desktop is no different.  To get your router to send Remote Desktop traffic back and forth between your home and work computers, you need to "open up" that port.  Your router will have a configuration section for this, look for "ports" or often "applications and games" if they are re-labeling to make things easier.  Once found, enable port 3389 for both incoming and outgoing traffic (TCP & UDP is fine).  You will see that you also need to specify your local computer's IP address.  You can't have more than one computer behind your router enabled for Remote Desktop outside of your home at the same time.  Just like with your ISP's provided IP address, your local one may change when you reboot as well.  You will need to keep this ports page updated with any changes.

Once you're configured, you should have no difficulty connecting from work, unless they block traffic on port 3389 in which case you will need to speak to your work's network administrator.  A word on your home security here.  Opening the port is fine for when you need it.  Close it when you don't.