>Which WiFi router under $50.00 US would be the platform. <
"White Box" from China, to be discussed.
As it needs quite some RAM (128/256) and Flash (8/16). I worked with different factories.
(A Western Digital myNet N600 would be OK, but not available any more.)
>What firmware platform would you use?<
openwrt
>Assurance that getting updated white and blacklist from the server would not be a problem. and redirecting, not just blocking can be accomplished<
2 possibilities: Using DNS (for domain based redirect only ) OR proxy for string-based redir.
How do you want https to be handled ?
BTW: I have completed such a project for parental control within my family.
Without string based filter, as it might stress the CPU too much. But no problem, to integrate.
Time to complete is based on assumption, that no additional requirements show up.
Web interface for local management is "no-frills", which means, functional, not necessarily "beautiful".
EXCLUDED from my bid is parsing logs in the router. This is definitely too much for a low cost device. Should be done on the server.
HW: One factory in China, the router of which I uased already for my own parental control, sells for about 25$ a suitable device, free of factory. Not very attractive, though, a real "White Box". However, OEM branding starting at 1000pcs., OR supply of customized enclosure.