The best budget PSU for my build?

Solution
A budget psu can become very expensive.
A cheap psu will not have the protective circuitry to protect your other parts from damage if it fails under load.
The power of a psu is mainly gated by the discrete graphics card.
Since you have none, 300w or better is appropriate.
Here is a list of psu quality tiers; Buy tier 1 or 2.

https://community.newegg.com/eggxpert/computer_hardware/f/135081/t/45344.aspx?Redirected=true

You buy a apu for the excellent graphics.
But plan on keeping it forever; there are no good update options.
If you buy a discrete graphics card, you negate the value of the apu.
Even if you do, there are no good cpu updates available to support a much stronger graphics card.
What you get is what you will have for a long time.
A budget psu can become very expensive.
A cheap psu will not have the protective circuitry to protect your other parts from damage if it fails under load.
The power of a psu is mainly gated by the discrete graphics card.
Since you have none, 300w or better is appropriate.
Here is a list of psu quality tiers; Buy tier 1 or 2.

https://community.newegg.com/eggxpert/computer_hardware/f/135081/t/45344.aspx?Redirected=true

You buy a apu for the excellent graphics.
But plan on keeping it forever; there are no good update options.
If you buy a discrete graphics card, you negate the value of the apu.
Even if you do, there are no good cpu updates available to support a much stronger graphics card.
What you get is what you will have for a long time.
 
Solution