For a "budget build", I think you guys are going overkill on the power supply. A system with these specs should never even draw 250 watts of power under load, so a PSU rated for up to 550 watts is unnecessary. Likewise, while being modular can make cable management a little easier, it tends to add more to the price for what could be handled by a few zip ties. In a budget build, that money would probably be better put toward hardware that can have more of an actual effect on performance, like a better graphics card or a larger SSD.
There are other, lower cost options for a PSU that could still be considered decent enough, such as this
EVGA 430 W1 100-W1-0430-KR 80+ WHITE 430W, currently on sale for $37 shipped at Newegg, with an additional $10 rebate. With the rebate, that comes to less than half the price, and this unit should be more than capable to handle a system like this. The cords aren't removable, but they're at least wrapped in a nice mesh.
Dropment :
I got recommended this build https://pcpartpicker.com/user/dropment/saved/hQXnQ7
I see you got suggested a slightly higher-powered PSU from the same series, and yeah, that would be another good lower-cost option, particularly if you don't want to deal with a rebate.
In my opinion, I'd go with a GTX 1060 in place of a 1050ti though, as it should provide better performance in newer and upcoming games, particularly if you want to play at higher resolutions, or with graphics settings maxed.
Also, the case in that build is pretty nice, though if you were looking to further reduce costs and are willing to put up with installing things in a smaller space, you could always go with a MicroATX case, as the other two builds here used.