Hi Silver, I'd like to join in congratulating you. Great way to get some exercise and save some money.

A few have already mentioned, but as far as your gf being uncomfortable on the seat, I'd say there is a 90% chance that more riding will fix that issue. If you are not used to it, a bike seat will be extremely uncomfortable and your rear end will be quite sore the first couple rides. After 2 or 3 rides though, you will start to get used to it. I also would not advise a cushion. I'd say bike shorts if anything, but mostly just time in the saddle works.

Rack and Panniers will be a godsend for you. Not only for biking to work, but they are great if you want to start picking up groceries, or running other errands. I started commuting, but now I love doing everything on my bike, to a point where I enjoy going out to get something as it's a chance to ride.

Stick with it, get a decent sent of panniers (some can be found cheap), or use what you got. Sometimes, a container and some bungees does the trick. Good luck!