Technically all CPUs with integrated graphics can be classified as APUs, or even SoCs.
Picking a CPU means going for a completely different set of hardware. So you should be looking at total cost of the CPU/Motherboard/Ram.
The Intel chips with the best integrated graphics are out of your price range, but the low end chips offer a good platform for later upgrades.
AMD's top end APU is kind of old, and there would be zero upgrade path. AMD's new lineup of APUs is yet to be released.