You can definitely do better with your money. Minecraft, Civ V, and Sims are all relatively easy to run so you could really get away with a Ryzen APU pretty easily. I would have to recommend an APU system right now, because buying GPUs new in the US currently, is impossible for a reasonable price. If you're willing to buy a used GPU, then you could get a pretty nice system for your money but if you're not willing to buy used parts, go with an APU system now and you can always add a discrete GPU later if you want/need.
Here's a decent starting point;
PCPartPicker part list / Price breakdown by merchant
CPU: AMD - Ryzen 5 2400G 3.6GHz Quad-Core Processor ($168.99 @ SuperBiiz)
Motherboard: ASRock - AB350 Pro4 ATX AM4 Motherboard ($86.89 @ OutletPC)
Memory: G.Skill - Ripjaws V Series 16GB (2 x 8GB) DDR4-3000 Memory ($179.89 @ OutletPC)
Storage: Crucial - MX500 500GB 2.5" Solid State Drive ($129.99 @ Amazon)
Case: Phanteks - Eclipse P300 Tempered Glass ATX Mid Tower Case ($59.49 @ Amazon)
Power Supply: SeaSonic - FOCUS Gold 550W 80+ Gold Certified Semi-Modular ATX Power Supply ($64.99 @ SuperBiiz)
Monitor: LG - 27UD58-B 27.0" 3840x2160 60Hz Monitor ($337.90 @ Amazon)
It's a little over budget, but that's because I included a 4k monitor and 16GB RAM, with a nice big SSD. The SSD, I'd leave as is, 500GB is plenty of storage and $130 is a reasonable price for a good 500GB SSD, you can always add an HDD later if you want/need more storage. If you really wanted to though, you could swap the 500GB SSD for a 240/250GB SSD and a 1TB HDD. You can drop down to 8GB RAM to save $80-90. 8GB is the bare minimum I'd recommend these days, and personally I wouldn't accept any less than 16GB in a personal system but you would be fine with 8GB, so it's up to you if you'd rather just save some money. I included a pretty nice case and PSU, both of which will easily last you a good few years if you want them to.
Here is an alternative monitor, 1440p instead of 4k, and $120 cheaper;
If you're comfortable buying a used GPU, then you can drop to the 1440p monitor, 8GB RAM and put the money saved towards a used GTX 970 or 980. If you do buy a GPU, swap the R5 2400G for an R5 1400 or R5 1600. Keep in mind that you will NEED the R5 2400G if you don't have a GPU, as the 2400G is the only Ryzen 5 CPU with integrated graphics.
Lastly, I'd recommend adding a Cryorig H7 to this system whenever you can afford it. The stock CPU cooler will be fine, but the H7 would definitely be a nice upgrade, especially if you're running an R5 2400G.