3400G is a waste of money, if you're going that direction I'd suggest the 2400G since it's like $80 cheaper and just about the same performance.What are the Ryzen 5's like? I was looking at the Ryzen 5 3400G for $239.
Otherwise I'd highly recommend a B450 motherboard with a Ryzen 3600 CPU. Just ask whoever you buy it from to update the BIOS, if it's Ryzen 3 ready it'll have a sticker on the box saying "RYZEN 3000 READY".
That's pretty much the ideal value combo, but you do need a graphics card. 2400G you don't need a graphics card.
3600 - $300
B450 - $100
16GB decent 3200MHz ram - $120
Case with a PSU built in - $100ish
You'd only need a storage drive after that really and a basic GPU which you can upgrade later if you need some heavier graphics horsepower.
That's pretty damn high end at a nice budget.
If you want to save a hundred or two, I'd go the same motherboard with a 2600 instead, or even a 2400G which are $199 $180 respectively, I would still keep the same motherboard though. With the 2400G you're saving $120 + the cost of a basic GPU so it's a decent budget option.