It sounds like you have an HP or other OEM pre-built system? That could be quite limiting as to what we can do due to the size of graphics card that can physically fit in there.
Your PSU wont allow much room for upgrading, a quick search seems to suggest its a low quality 250watt unit that's maybe 10 years old. I think its ATX sized though, which means we should be able to replace it easily, and potentially pair it with a newer low profile GPU without spending the earth.
Could you post some pictures of your system with the side off so we can have an idea what we are working with? You'd need to upload pictures to a hosting service like Imgur and link them here
Its would also be good to know what kind of games would you want to play specifically, what's your maximum budget for upgrades, and what country you are in?