You need 200-300W inverter because you might want to run something else, ex. laptop or MP4 video player at the same time.
Preferably PSW. $20 MSW may or may not work with TV, laptop and player could have problems too. They all get warm, and often have fans, so make sure yours is fan-less (unless installed where you can't hear it).
Preferably with dedicated 110V inverter outlet or powerbar close to TV and other electronics.
I would leave 12V to permanent 12V devices. For charging a phone via USB, you can get $1 adapter on Ebay
https://www.ebay.com/itm/5V-USB-Car-Cigarette-Lighter-DC-Power-Charger-Car-Adapter-for-Iphone-Cell-Phone/382011298326?hash=item58f1a5d216:g:5HUAAOxyBotTadIe:rk:4:pf:1&LH_BIN=1&frcectupt=true