combining Wi-Fi and hard wired routers

yes it is safe , we do it all the time , look at 99% of the posts in the network forum (which i have moved your post to) and you will see the ipconfig /all - and probably the same numbers as you have - I want to check if its a modem only or a modem router you have


yes

i dont have a recommendation, all the main brands are good - dlink, linksys, netgear, belkin etc
also will depend on your current modem

ATT provides your broadband - they may provide one for free , most ISP in the UK do that , if if you are an old customer who only has a modem or older device , you can usually (not always) get a new router for free from them , by renewing your contract for a further 12months / year - although in the US , I believe some ISP rent the device , and i would not recommend that

Some ISP will provide very limited support , if/when something goes wrong, with a non approved router.

It maybe worth have a discussion with the ATT loyalty team or retention team - not just the usual call desk, they wont help normally.