Pretty much every AMD CPU has the same per core performance, and none of them compare to an i3 aside from like the 9590
Your best bet for an AMD CPU for low budget is going to be the 860K, which is a bit slowly, but cheaper than an i3 naturally, you'll also want a 78 or 88X motherboard for it
What's the desktop build going to be used for and what's the budget?
Well then, ya, here, just upgrade the CPU to a 5350 and you should be good to go for a low power office PC, if you just wanna spend a little more for a faster CPU then the A8 7600 is going to be your best bet for FM2+
You could also look into a case like this for the AM1 PC, it's not much better than the ITX board itself
As an owner of 2 APUs they are plenty for web browsing and office. To be completely honest the AM1 platform was built for office and web browsing. Personally I'd go with the Athlon or the A8-7700K
Skylake, because why not, were building a new system. Not like there's any huge price difference between G3258 and the G4400. And since this is for web/office you're likely not going to even overclock so.. mITX because other builds are mITX. DDR4 is pretty much about the same price as DDR3 nowadays. 1x8GB to leave the door open for 16GB. Not like you're gonna see any perf difference in office use between single and dual channel.. SSD, well it's an SSD. TLC but shouldn't really matter for office use.. No clue about this case, just picked it since Streetguru had picked it. I'll rather buy some OEM PSU from Seasonic. It's 80+ Bronze because why not.
And here's a mATX build since if it doesn't have to be mITX then your motherboard options become cheaper.. http://pcpartpicker.com/p/fdkGyc 265USD
Motherboard just a placeholder, just look at the different motherboards available (socket 1151) and see what connections and features they have. Choose accordingly. For the case I'd recommend the Silverstone PS09B, it's not the smallest mATX case but quite small still at 25 liters from external dimensions compared to 15 liters of that mITX case. It's what I would call a "quiet case". In essence, the front intake fan is properly behind the front panel and there's not a direct route for noise to escape. And it's cheap.
Here's Anandtech Bench for SYSMark 2014, office productivity. http://anandtech.com/bench/CPU/1030 Find the G3420 (Haswell, 2x3.2Ghz) from there and add a few percent to get G4400 (Skylake, 2x3.3Ghz).