If I explain a wee bit about how computers work it might help a bit?
The CPU is the Central Processing Unit, the higher the GHz, the faster it processes. For looking up stuff on the internet or using email and doing homework, you don't need high speeds, if you want to use it for gaming like Minecraft and other games, the speed of the processor helps to keep the game running. They tend to come in dual core or quad core - like before the higher the number the better.
The amount of RAM (random access memory) is also important for gaming, again this affects how quickly the game will play. Higher number the better.
GPU or Graphics is what affects how the game displays and also affects the speed. Dedicated graphics are usually better than on-board graphics but there is a long history of different graphics cards...
Storage is the HDD or SSD, for general use again you may not need very much but the system itself will use some so if there isn't much then you could be looking at having to store things on memory sticks. Games use more memory for the saves. Most proper gamers will be using Steam etc which will (I think) save their progress so it doesn't use up space on the PC itself.
Windows 10 is the operating system and is the most up to date.
Open Office is basically free microsoft office with less functionality. I don't use anything else and it's perfectly fine. You can save documents as microsoft versions if you need to pass them on to teachers etc.
I cant see anything in your budget that would play minecraft well.
The main issue you may have with a refurb is the battery. Sometimes the batteries don't last that well and it means that you really need to be plugged in. Not necessarily an issue though.