@iEllaLouise You did not mention your hard drive space but 256 gb ssd is too small to game on if you have no other hard drive. The sims 3 takes advantage of an ssd but the sims 4 does not. These games"Require" gaming computer hardware. You need a gaming laptop or desktop. You have to game plugged in even if you have a laptop. If your gaming on battery will make the game even worse than just having low end specs. The battery is for light computer tasks or streaming a movie only. Not for gaming. you need extra power to game.
Desktop to build yourself with all modern hardware will not be cheaper, you will just have better hardware than buying something mass produced off the shelf. If you want an ssd you need one large enough to game on. You want at least 500 gb ssd. These are not cheap.
SSD is faster than HDD however only the sims 3 loads quicker on SSD. The sims 4 does not. SSD is good for booting windows and other programs quicker. Your SSD at the moment is too small to game on. Your video card is lower end and your laptop has no cooling. If you have a low end budget it's better to have hardware inside the computer that can run the game. SSD would be last on the list. Video card, processor , and ram are more important than the SSD. The more features you want in a computer, the more it will cost you.