Whoa. That escalated pretty quick. For the person trying to mod, thanks but no need. Please use the report button and leave it alone. If the OP was a giant jerk and replied negatively to your post things could have got ugly. We agreed to verbal abuse when we agreed to do this.
For the OP, or original poster, i don't see the need for a new machine. Your APU/CPU is based on really old tech that has been greatly improved on, but as you said your demands aren't that great. I already correctly guessed your monitor size and suggested gpu upgrade, the 2060. That card is at the extreme upper end of what I'd pair with your APU.
I would normal say just upgrade the gpu, but the psu could be an issue. You have a lower end system so the psu could be lower end as well. You've called it a 500W, 550W, and said you don't know which it is. Before i suggest a gpu i always like knowing what the psu is. Not because i want to gloat about how much better mine is, but because i don't want to harm your system. If you take the side of your tower off you can see the big box with wires coming out. Will probably say something like thermaltake, antec, seasonic, etc. With of course the wattage listed somewhere. If you can give us the model number that would be great.
I wouldn't bother with the 1650s. I don't know of any 6gb model. A 1660S or other such card would be good. Waiting for AMDs next big card is also a good idea. Finally people run multiple hard drives because they put windows and games on the faster SSD, while docs, music, etc goes on the slower HDD.